EMTeachline interactive algebra software - solving algebra problems
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EMMentor Algebra

EMMentor Algebra
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Get a private math tutor right on your desk! All students need help at some point, so be sure to get the help you need. With dozens of interactive learning techniques and a unique system of error analysis, EMMentor provides a qualified training of problem solving skills. He will offer you a task, ask you questions, give you hints as you need them, analyse your answers, trace your errors, detect gaps in your theoretical knowledge and problem solving skills and generate optimal exercises to close these gaps. EMMentor is here to help you figure out how to learn math for yourself. Those who stick with EMMentor will come away with a stronger understanding of fundamental math concepts, improved higher-level thinking skills and excellent practical skills in solving math problems! Free fully functional downloadable version of EMMentor is available. Our online demos enable you to try a number of training techniques and observe examples of error analysis.



Parameters of the program
Name of program:
EMMentor_Algebra
Number of problems:
70439
Number of similar variants:
12
Languages of interface:
English, German
Price:
222 EUR
Size of archive:
5389 kb

Abstract. EMMentor_Algebra is a new generation interactive training program that offers a large number of math problems, a variety of appropriate techniques to solve problems and a unique system of performance analysis with methodical feedback. Students at all levels can practice at their own pace, review their own work, monitor their weaknesses and achievements, and get methodical recommendations for building missing math knowledge and skills.Considered are algebraic problems: computational problems, proofs of identities and solutions of equations and inequalities. Thematically, this program integrates Algebra_Calculation, Algebra_Identity, Algebra_Proof_Inequalities, Algebra_Equations and Algebra_Inequalities. The program includes 70439 math problems of 11 levels of complexity, from basic to advanced. For each math problem, EMMentor offers a set of methodical tasks to be discharged at each step of problem solution. Your work will be throughly analysed with respect to multiple parameters. You can review the distributions of your errors throughout the solution steps, over formulas and other math concepts, over topics, etc. Based on this joint error distribution, EMMentor provides an optimal set of tasks for error correction. In addition, EMMentor offers a number of test authoring options that automate creation of math tests, quizzes, homeworks and exams of varied complexity and enable automatic generation of a number of variants around each test. The tests with or without the solutions can be printed out or stored in a file and re-used. Dozens of variant tests are ready for students to review and reinforce their math skills. Each definition, rule etc can be instantly translated to German or another available language.


System Requirements:

Pentium 2 or higher

64 MB RAM

Windows 98 or higher

Internet Explorer 5.5 or higher

Plug-in MathPlayer (downloadable from here)


Program's detail
Examples
Press release
Contents of the program
Characteristics of similar programs

Examples

An online sample of math problems and problem solutions from this program is provided below:

Problems: Algebra

back EMTEACHLINE MATHEMATICS SOFTWARE - YOUR PERSONAL MATH TEACHER

Press release

ABSTRACT. EMTeachline Software has released a PC-based interactive mathematics software brand EMMentor that tutors in solving math problems. This encyclopedic software contains hundreds thousands of fully explained step by step solutions to math problems from basic to advanced and thousands of related definitions, rules, formulas and theorems. Based on a unique teaching technology, EMMentor controls, analyses and grades your performance, detects gaps in your theoretical knowledge and problem-solving skills, and generates an optimal set of tasks to close the revealed gaps. This software helps kids grasp math concepts and build problem solving skills much more effectively than any classroom teacher. For teachers and parents, EMMentor offers a comprehensive objective analysis of children's performance, with tables and plots, and methodical recommendations for error correction. Easy-to-use authoring options automate development of math tests and homeworks. The software is designed for mathematics self-study. Provides an ideal help for math teachers. Suitable for elementary, middle and high school use.

1. SOFTWARE OVERVIEW

The EMTeachline Interactive Mathematics Software EMMentor provides kids and teens with the chance to build outstanding problem-solving skills in math without any external help. Based on a brand-new teaching technology, this highly interactive software will help you much more effectively than any classroom teacher.

EMMentor includes a set of original interactive training techniques and a unique system of performance analysis with methodical feedbacks. Each technique consists of a set of questions asked at each step of task performance and a system of multiple choice answers with hints. Based on an analysis of your answers, the software detects gaps in your theoretical knowledge and problem-solving skills and summarises your errors. To correct errors and develop missing skills, EMMentor offers an optimal set of exercises.

The error analysis is made for a particular task performance, as well as for a number of tasks performed during the selected period of time. EMMentor shows, in tables and on plots, how many errors were made and how many hints were used at each step of solution within one technique, the distributions of errors and hints throughout the techniques, over formulas and other math categories, the total number of errors per topic, etc. The concluding methodical recommendations are based on an objective analysis of these joint error distributions. Any teacher or tutor will find this function to be extremely useful.

As a multilingual tutoring program, EMMentor offers a way for children to learn math lexicon in a foreign language. Translation of any text to German or another available language is easily obtained by double-clicking on it. Those kids who study not in a native language will find this option invaluable.

Covered subject areas are arithmetic, pre-algebra, algebra, trigonometry and hyperbolic trigonometry. All math problems are graded in 11 complexity classes from basic to advanced and provided with fully explained step by step solutions. Comprehensive tutoring material is provided for each solution step. The available test authoring options automate development of tests, quizzes, homeworks and exams. All developed materials can be printed out or stored in a file and re-used.

2. SKILLS COVERED

Arithmetic and Pre-Algebra: Operations: multiplication, division, addition, subtraction. Fractions, powers. Numeric expressions: estimation, equivalencies, problem-solving. Solving arithmetic problems using algebraic formulas.

Algebra: Polynomial and fractional rational expressions: transformation, simplification, evaluation. Solution of linear, quadratic, cubic, biquadratic, reciprocal and fractional algebraic equations and inequalities. Proofs of algebraic identities. Solution methods: Substitution, factoring, grouping, Bezout theorem, formulas of short multiplication, method of intervals and more. Related theory: definitions and rules, proof of algebraic formulas and theorems.

Trigonometry and Hyperbolic Trigonometry: trigonometric and hyperbolic functions, arcus functions. Trigonometric and hyperbolic expressions: transformation, simplification, evaluation. Solution of trigonometric and hyperbolic equations. Proofs of trigonometric and hyperbolic identities. Solution methods: universal substitution, sum, product and addition of trigonometric functions, power reduction, multiple argument, shift of argument and more. Related theory: definitions and rules, proof of trigonometric and hyperbolic formulas.

3. USER OPTIONS

For math students: You will get a diagnosis of all vacancies in your math skills. You can train the missing problem solving skills with the help of dozens of interactive training techniques. You can effectively learn definitions, rules and other math concepts, study solution methods, pick up skills of verbal formulation of math transformations, learn proofs of math formulas and theorems, develop reasoning skills etc. And in parallel, you can learn math lexicon in a foreign language!

For math teachers: You can use an extensive bank of math problems; arrange problems by topic, complexity level, solution method and type of task; compile math tests, quizzes, homeworks and exams of varied complexity; create your own didactic materials and problem-solving lesson plans; generate numerous similar variants of math tests; use dozens of ready variant tests. For each student of yours, you can get an objective analysis of his/her work, revealing his/her weak and strong points, together with an optimal set of tasks for error correction.


back Contents of the program

Themes

Chapters and sections
back Rational expressions. Computational problems
Chapters
Sections

Evaluation of linear expressions and expressions reduced to them

  • Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Distributive law. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Fractional expressions reduced to linear expressions. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law. Evaluation
  • Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Formulas of short multiplication. Evaluation

Evaluation of quadratic expressions and expressions reduced to them

  • Evaluation of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Integer coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Formulas of short multiplication. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Rational coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Factorization of quadratic trinomial. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Properties of powers. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Grouping method. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Integer coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients. Evaluation
  • Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Factorization of quadratic trinomial. Evaluation

Evaluation of algebraic high-degree expressions

  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Integer roots. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Irrational roots. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Integer roots. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Grouping method. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Perfect square. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Irrational roots. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Formulas of short multiplication. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Difference of squares. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Factorization of quadratic trinomial. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Properties of fractions. Evaluation
  • Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Difference and sum of cubes. Evaluation

Evaluation of fractional algebraic expressions

  • Evaluation of fractional algebraic expressions. Elementary fractional algebraic expressions. Evaluation
  • Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator. Evaluation
  • Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. Evaluation
  • Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator. Evaluation
  • Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator. Evaluation
  • Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Evaluation

Comparison of values of linear expressions and expressions reduced to them

  • Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities
  • Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Distributive law
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of powers. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Rational coefficients. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Rational coefficients. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Factorization of quadratic trinomial. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Distributive law. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Formulas of short multiplication. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of fractions. Distributive law. Comparison of values
  • Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of fractions. Formulas of short multiplication. Comparison of values

Comparison of values of quadratic expressions and expressions reduced to them

  • Comparison of values of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Comparison
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare quadratic expressions containing fractions
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Integer coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Formulas of short multiplication
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Rational coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Factorization of quadratic trinomial
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Properties of powers
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Grouping method
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients
  • Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Factorization of quadratic trinomial

Comparison of values of algebraic high-degree expressions

  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Bezout theorem. Irrational roots
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Bezout theorem. Integer roots
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Grouping method
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Perfect square
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Formulas of short multiplication
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Difference of squares
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Factorization of quadratic trinomial
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Properties of fractions
  • Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Difference and sum of cubes

Comparison of values of fractional algebraic expressions

  • Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with linear expression in numerator
  • Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with quadratic expression in numerator
  • Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with cubic expression in numerator
  • Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator

back Rational expressions. Transformations and proofs
Chapters
Sections

Transformation of linear expressions and expressions reduced to them

  • Transformation of linear expressions and expressions reduced to them. Elementary linear expressions
  • Transformation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Distributive law
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers
  • Transformation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
  • Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
  • Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication

Transformation of quadratic algebraic expressions and expressions reduced to them

  • Transformation of quadratic algebraic expressions and expressions reduced to them. Elementary quadratic expressions
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions containing fractions
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Decomposition of quadratic trinomial
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Grouping method
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Factorization of quadratic trinomial
  • Transformation of quadratic algebraic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Integer coefficients

Transformation of algebraic high-degree expressions

  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Irrational roots
  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
  • Transformation of algebraic high-degree expressions. High degrees. Grouping method
  • Transformation of algebraic high-degree expressions. High degrees. Perfect square
  • Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
  • Transformation of algebraic high-degree expressions. High degrees. Formulas of short multiplication
  • Transformation of algebraic high-degree expressions. High degrees. Difference of squares
  • Transformation of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial
  • Transformation of algebraic high-degree expressions. High degrees. Properties of fractions
  • Transformation of algebraic high-degree expressions. High degrees. Difference and sum of cubes

Transformation of fractional algebraic expressions

  • Transformation of fractional algebraic expressions. Elementary fractional algebraic expressions
  • Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator
  • Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator
  • Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator
  • Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator
  • Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator
  • Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

Factorization of linear expressions and expressions reduced to them

  • Factorization of linear expressions and expressions reduced to them. Elementary linear expressions
  • Factorization of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Distributive law
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Properties of powers
  • Factorization of linear expressions and expressions reduced to them. Expressions reduced to linear expressions
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
  • Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
  • Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication

Factorization of quadratic expressions and expressions reduced to them

  • Factorization of quadratic expressions and expressions reduced to them. Elementary quadratic expressions
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

Factorization of algebraic high-degree expressions

  • Factorization of algebraic high-degree expressions. High degrees. Grouping method
  • Factorization of algebraic high-degree expressions. High degrees. Perfect square
  • Factorization of algebraic high-degree expressions. High degrees. Formulas of short multiplication
  • Factorization of algebraic high-degree expressions. High degrees. Difference of squares
  • Factorization of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial
  • Factorization of algebraic high-degree expressions. High degrees. Properties of fractions
  • Factorization of algebraic high-degree expressions. High degrees. Difference and sum of cubes

Proof of identity. Linear expressions and expressions reduced to them

  • Proof of identity. Linear expressions and expressions reduced to them. Elementary linear expressions
  • Proof of identity. Linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Distributive law
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Properties of powers
  • Proof of identity. Linear expressions and expressions reduced to them. Expressions reduced to linear expressions
  • Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
  • Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
  • Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
  • Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
  • Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law

Proof of identity. Quadratic expressions and expressions reduced to them

  • Proof of identity. Quadratic expressions and expressions reduced to them. Elementary quadratic expressions
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
  • Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Grouping method
  • Proof of identity. Quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Integer coefficients
  • Proof of identity. Quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Rational coefficients

Proof of identity. High-degree expressions

  • Proof of identity. High-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
  • Proof of identity. High-degree expressions. High degrees. Bezout theorem. Irrational roots
  • Proof of identity. High-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
  • Proof of identity. High-degree expressions. High degrees. Grouping method
  • Proof of identity. High-degree expressions. High degrees. Perfect square
  • Proof of identity. High-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
  • Proof of identity. High-degree expressions. High degrees. Formulas of short multiplication
  • Proof of identity. High-degree expressions. High degrees. Difference of squares
  • Proof of identity. High-degree expressions. High degrees. Properties of fractions

Proof of identity. Fractional algebraic expressions

  • Proof of identity. Fractional algebraic expressions. Elementary fractional algebraic expressions
  • Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator
  • Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator
  • Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator
  • Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator

back Rational expressions. Proofs of inequalities
Chapters
Sections

Proof of strict inequalities. Linear expressions and expressions reduced to them

  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Distributive law
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Properties of powers
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Rational coefficients
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Rational coefficients
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Factorization of quadratic trinomial
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Distributive law
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Formulas of short multiplication
  • Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Properties of powers

Proof of strict inequalities. Quadratic expressions

  • Proof of strict inequalities. Quadratic expressions. Elementary quadratic inequalities
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities containing fractions
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Distributive law. Integer coefficients
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Grouping method
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Integer coefficients
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Rational coefficients
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Grouping method
  • Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Factorization of quadratic trinomial
  • Proof of strict inequalities. Quadratic expressions. Fractional inequalities. Method of substitution. Distributive law. Integer coefficients

Proof of strict inequalities. Algebraic high-degree expressions

  • Proof of strict inequalities. Algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
  • Proof of strict inequalities. Algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems

Proof of strict inequalities. Fractional algebraic expressions

  • Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator. To prove inequality
  • Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. To prove inequality

back Rational equations
Chapters
Sections

Linear equations

  • Linear equations. Elementary linear equations
  • Linear equations. Linear equations containing fractions
  • Linear equations. Linear equations. Distributive law
  • Linear equations. Equations reduced to linear equations. Formulas of short multiplication
  • Linear equations. Linear equations. Formulas of short multiplication. Cubes
  • Linear equations. Linear equations. Properties of powers
  • Linear equations. Equations reduced to linear equations
  • Linear equations. Homographic equations with rational coefficients. Properties of fractions
  • Linear equations. Homographic equations with integer coefficients. Properties of fractions
  • Linear equations. Homographic equations with integer coefficients. Method of substitution
  • Linear equations. Homographic equations with rational coefficients. Method of substitution
  • Linear equations. Linear equations. Factorization of quadratic trinomial
  • Linear equations. Equations reduced to linear. Method of substitution. Distributive law
  • Linear equations. Equations reduced to linear. Method of substitution. Distributive law. Formulas of short multiplication

Quadratic equations

  • Quadratic equations. Elementary quadratic equations
  • Quadratic equations. Quadratic equations containing fractions
  • Quadratic equations. Equations with integer coefficients. Distributive law
  • Quadratic equations. Quadratic equations. Formulas of short multiplication
  • Quadratic equations. Quadratic equations with rational coefficients. Distributive law
  • Quadratic equations. Equations reduced to quadratic. Factorization of quadratic trinomial
  • Quadratic equations. Equations reduced to quadratic. Properties of powers
  • Quadratic equations. Fractional algebraic equations reduced to quadratic equations. Distributive law
  • Quadratic equations. Equations. Grouping method
  • Quadratic equations. Equations. Method of substitution. Distributive law. Integer coefficients
  • Quadratic equations. Equations. Method of substitution. Distributive law. Rational coefficients
  • Quadratic equations. Equations. Method of substitution. Formulas of short multiplication
  • Quadratic equations. Equations. Method of substitution. Properties of fractions
  • Quadratic equations. Equations. Method of substitution. Grouping method
  • Quadratic equations. Equations. Method of substitution. Factorization of quadratic trinomial
  • Quadratic equations. Fractional equations. Method of substitution. Distributive law
  • Quadratic equations. Fractional equations reduced to quadratic equations. Method of substitution
  • Quadratic equations. Fractional equations. Method of substitution. Formulas of short multiplication
  • Quadratic equations. Fractional algebraic equations reduced to quadratic equations. Formulas of short multiplication

Cubic equations

  • Cubic equations. Cubic equations in reduced form
  • Cubic equations. Cubic equations in general form

Algebraic equations. Method of substitution

  • Algebraic equations. Method of substitution. Elementary biquadratic equations
  • Algebraic equations. Method of substitution. Algebraic equations reduced to biquadratic equations
  • Algebraic equations. Method of substitution. Algebraic equations. Linear substitution
  • Algebraic equations. Method of substitution. Algebraic equations. Quadratic substitution
  • Algebraic equations. Method of substitution. Algebraic equations. Homographic substitution
  • Algebraic equations. Method of substitution. Reciprocal equations
  • Algebraic equations. Method of substitution. Algebraic equations reduced to reciprocal

Algebraic high-degree equations

  • Algebraic high-degree equations. High-degree equations. Bezout theorem. Integer roots
  • Algebraic high-degree equations. High-degree equations. Bezout theorem. Irrational roots
  • Algebraic high-degree equations. High-degree equations reduced to the form allowing application of the Bezout theorem. Integer roots
  • Algebraic high-degree equations. High-degree equations. Grouping method
  • Algebraic high-degree equations. High-degree equations. Perfect square
  • Algebraic high-degree equations. High-degree equations reduced to the form allowing application of the Bezout theorem. Irrational roots
  • Algebraic high-degree equations. High-degree equations. Formulas of short multiplication
  • Algebraic high-degree equations. High-degree equations. Difference of squares
  • Algebraic high-degree equations. High-degree equations. Factorization of quadratic trinomial
  • Algebraic high-degree equations. High-degree equations. Properties of fractions
  • Algebraic high-degree equations. High-degree equations. Difference and sum of cubes
  • Algebraic high-degree equations. High-degree equations. Method of substitution

Fractional algebraic equations

  • Fractional algebraic equations. Elementary fractional algebraic equations
  • Fractional algebraic equations. Fractional algebraic equations reduced to linear equations
  • Fractional algebraic equations. Fractional algebraic equations reduced to quadratic equations
  • Fractional algebraic equations. Fractional algebraic equations reduced to cubic equations
  • Fractional algebraic equations. Fractional algebraic equations reduced to biquadratic equations
  • Fractional algebraic equations. Fractional algebraic equations reduced to reciprocal equations
  • Fractional algebraic equations. Fractional algebraic equations reduced to quadratic equations. Method of substitution
  • Fractional algebraic equations. Fractional algebraic equations. Method of substitution

back Rational inequalities
Chapters
Sections

Weak linear inequalities

  • Weak linear inequalities. Elementary linear weak inequalities
  • Weak linear inequalities. Linear weak inequalities containing fractions
  • Weak linear inequalities. Homographic weak inequalities. Method of substitution. Rational coefficients
  • Weak linear inequalities. Linear weak inequalities. Distributive law
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Formulas of short multiplication
  • Weak linear inequalities. Linear weak inequalities. Formulas of short multiplication. Cubes
  • Weak linear inequalities. Linear weak inequalities. Properties of fractions
  • Weak linear inequalities. Linear weak inequalities. Factorization of quadratic trinomial
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Distributive law
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Properties of powers
  • Weak linear inequalities. Linear weak inequalities. Properties of powers
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities
  • Weak linear inequalities. Fractional weak inequalities reduced to linear inequalities
  • Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Rational coefficients
  • Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Integer coefficients
  • Weak linear inequalities. Homographic weak inequalities. Method of substitution. Integer coefficients
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Distributive law
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Properties of powers
  • Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial

Strict linear inequalities

  • Strict linear inequalities. Elementary strict linear inequalities
  • Strict linear inequalities. Strict linear inequalities containing fractions
  • Strict linear inequalities. Strict linear inequalities. Distributive law
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication. Cubes
  • Strict linear inequalities. Strict linear inequalities. Properties of fractions
  • Strict linear inequalities. Strict linear inequalities. Properties of powers
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities
  • Strict linear inequalities. Strict fractional inequalities reduced to linear inequalities
  • Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Rational coefficients
  • Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Integer coefficients
  • Strict linear inequalities. Strict homographic inequalities. Method of substitution. Integer coefficients
  • Strict linear inequalities. Strict homographic inequalities. Method of substitution. Rational coefficients
  • Strict linear inequalities. Strict linear inequalities. Factorization of quadratic trinomial
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Distributive law
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Properties of powers
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Distributive law
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Properties of powers
  • Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial

Strict quadratic inequalities

  • Strict quadratic inequalities. Elementary quadratic strict inequalities
  • Strict quadratic inequalities. Quadratic strict inequalities containing fractions
  • Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Rational coefficients
  • Strict quadratic inequalities. Strict inequalities. Distributive law. Integer coefficients
  • Strict quadratic inequalities. Strict inequalities. Formulas of short multiplication
  • Strict quadratic inequalities. Strict inequalities. Distributive law. Rational coefficients
  • Strict quadratic inequalities. Strict inequalities. Factorization of quadratic trinomial
  • Strict quadratic inequalities. Strict inequalities. Properties of powers
  • Strict quadratic inequalities. Fractional strict algebraic inequalities reduced to quadratic inequalities
  • Strict quadratic inequalities. Strict inequalities. Grouping method
  • Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Integer coefficients
  • Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
  • Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Integer coefficients
  • Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Rational coefficients
  • Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients

Weak quadratic inequalities

  • Weak quadratic inequalities. Elementary quadratic weak inequalities
  • Weak quadratic inequalities. Quadratic weak inequalities containing fractions
  • Weak quadratic inequalities. Weak inequalities. Distributive law. Integer coefficients
  • Weak quadratic inequalities. Weak inequalities. Formulas of short multiplication
  • Weak quadratic inequalities. Weak inequalities. Distributive law. Rational coefficients
  • Weak quadratic inequalities. Weak inequalities. Factorization of quadratic trinomial
  • Weak quadratic inequalities. Weak inequalities. Properties of powers
  • Weak quadratic inequalities. Fractional algebraic weak inequalities reduced to quadratic inequalities
  • Weak quadratic inequalities. Weak inequalities. Grouping method
  • Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Integer coefficients
  • Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Rational coefficients
  • Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
  • Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Integer coefficients
  • Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Rational coefficients
  • Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
  • Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients

Strict algebraic high-degree inequalities

  • Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Integer roots
  • Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Irrational roots
  • Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Integer roots
  • Strict algebraic high-degree inequalities. Strict high-degree inequalities. Grouping method
  • Strict algebraic high-degree inequalities. Strict high-degree inequalities. Perfect square
  • Strict algebraic high-degree inequalities. Strict inequalities. Formulas of short multiplication
  • Strict algebraic high-degree inequalities. Strict inequalities. Difference of squares
  • Strict algebraic high-degree inequalities. Strict inequalities. Factorization of quadratic trinomial
  • Strict algebraic high-degree inequalities. Strict inequalities. Properties of fractions
  • Strict algebraic high-degree inequalities. Strict inequalities. Difference and sum of cubes

Weak algebraic high-degree inequalities

  • Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Integer roots
  • Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Irrational roots
  • Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Integer roots
  • Weak algebraic high-degree inequalities. Weak high-degree inequalities. Grouping method
  • Weak algebraic high-degree inequalities. Weak high-degree inequalities. Perfect square
  • Weak algebraic high-degree inequalities. Weak inequalities. Formula of difference of squares
  • Weak algebraic high-degree inequalities. Weak inequalities. Factorization of quadratic trinomial
  • Weak algebraic high-degree inequalities. Weak inequalities. Properties of fractions
  • Weak algebraic high-degree inequalities. Weak inequalities. Difference and sum of cubes

Strict fractional inequalities

  • Strict fractional inequalities. Elementary fractional strict algebraic inequalities
  • Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict linear inequalities
  • Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities
  • Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities. Method of substitution

Weak fractional inequalities

  • Weak fractional inequalities. Elementary fractional weak algebraic inequalities
  • Weak fractional inequalities. Fractional weak algebraic inequalities reduced to linear inequalities
  • Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities
  • Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities. Method of substitution

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