 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 higherlevel 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_short

Number of problems:

9440

Number of similar variants:

3

Languages of interface:

English, German

Price:

143 EUR

Size of archive:

4396 kb

Abstract. EMMentor_Algebra_short 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_short, Algebra_Identity_short, Algebra_Proof_Inequalities_short, Algebra_Equations_short and Algebra_Inequalities_short. The program includes 9440 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 reused. 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
Plugin MathPlayer (downloadable from here)
Program's detail
Examples
An online sample of math problems and problem solutions from this program is provided below:
EMTEACHLINE MATHEMATICS SOFTWARE  YOUR PERSONAL MATH TEACHER
Press release
ABSTRACT. EMTeachline Software has released a PCbased 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 problemsolving 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. Easytouse authoring options automate development of math tests and homeworks. The software is designed for mathematics selfstudy. 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 problemsolving skills in math without any external help. Based on a brandnew 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 problemsolving 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 doubleclicking on it. Those kids who study not in a native language will find this option invaluable.
Covered subject areas are arithmetic, prealgebra, 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 reused.
2. SKILLS COVERED
Arithmetic and PreAlgebra: Operations: multiplication, division, addition, subtraction. Fractions, powers. Numeric expressions: estimation, equivalencies, problemsolving. 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 problemsolving 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.
Contents of the program
Themes
Chapters and sections
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 highdegree expressions

 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Integer roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Irrational roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Integer roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Grouping method. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Perfect square. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Irrational roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Formulas of short multiplication. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Difference of squares. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Factorization of quadratic trinomial. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Properties of fractions. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree 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 highdegree expressions

 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Bezout theorem. Irrational roots
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Bezout theorem. Integer roots
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Grouping method
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Perfect square
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Formulas of short multiplication
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Difference of squares
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Factorization of quadratic trinomial
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Properties of fractions
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree 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

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 highdegree expressions

 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Irrational roots
 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
 Transformation of algebraic highdegree expressions. High degrees. Grouping method
 Transformation of algebraic highdegree expressions. High degrees. Perfect square
 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
 Transformation of algebraic highdegree expressions. High degrees. Formulas of short multiplication
 Transformation of algebraic highdegree expressions. High degrees. Difference of squares
 Transformation of algebraic highdegree expressions. High degrees. Factorization of quadratic trinomial
 Transformation of algebraic highdegree expressions. High degrees. Properties of fractions
 Transformation of algebraic highdegree 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 highdegree expressions

 Factorization of algebraic highdegree expressions. High degrees. Grouping method
 Factorization of algebraic highdegree expressions. High degrees. Perfect square
 Factorization of algebraic highdegree expressions. High degrees. Formulas of short multiplication
 Factorization of algebraic highdegree expressions. High degrees. Difference of squares
 Factorization of algebraic highdegree expressions. High degrees. Factorization of quadratic trinomial
 Factorization of algebraic highdegree expressions. High degrees. Properties of fractions
 Factorization of algebraic highdegree 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. Highdegree expressions

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

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 highdegree expressions

 Proof of strict inequalities. Algebraic highdegree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
 Proof of strict inequalities. Algebraic highdegree 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

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 highdegree equations

 Algebraic highdegree equations. Highdegree equations. Bezout theorem. Integer roots
 Algebraic highdegree equations. Highdegree equations. Bezout theorem. Irrational roots
 Algebraic highdegree equations. Highdegree equations reduced to the form allowing application of the Bezout theorem. Integer roots
 Algebraic highdegree equations. Highdegree equations. Grouping method
 Algebraic highdegree equations. Highdegree equations. Perfect square
 Algebraic highdegree equations. Highdegree equations reduced to the form allowing application of the Bezout theorem. Irrational roots
 Algebraic highdegree equations. Highdegree equations. Formulas of short multiplication
 Algebraic highdegree equations. Highdegree equations. Difference of squares
 Algebraic highdegree equations. Highdegree equations. Factorization of quadratic trinomial
 Algebraic highdegree equations. Highdegree equations. Properties of fractions
 Algebraic highdegree equations. Highdegree equations. Difference and sum of cubes
 Algebraic highdegree equations. Highdegree 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

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 highdegree inequalities

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

Weak algebraic highdegree inequalities

 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Bezout theorem. Integer roots
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Bezout theorem. Irrational roots
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Bezout theorem. Integer roots
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Grouping method
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Perfect square
 Weak algebraic highdegree inequalities. Weak inequalities. Formula of difference of squares
 Weak algebraic highdegree inequalities. Weak inequalities. Factorization of quadratic trinomial
 Weak algebraic highdegree inequalities. Weak inequalities. Properties of fractions
 Weak algebraic highdegree 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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