 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_Hyperbolic

Number of problems:

33508

Number of similar variants:

3

Languages of interface:

English, German

Price:

174 EUR

Size of archive:

7121 kb

Abstract. EMMentor_Hyperbolic 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 hyperbolic problems: computational problems, proofs of identities and solutions of equations. Thematically, this program integrates Hyperbolic_Calculation, Hyperbolic_Identity and Hyperbolic_Equations. The program includes 33508 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
Hyperbolic 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. 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. 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 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. 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. Rational coefficients. 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. 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 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

Hyperbolic 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 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 algebraic highdegree expressions. High degrees. 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. 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. 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 identities related with linear expressions and expressions reduced to them

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

Proof of identities related with quadratic expressions and expressions reduced to them

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

Proof of identities related with highdegree expressions

 Proof of identities related with highdegree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
 Proof of identities related with highdegree expressions. High degrees. Bezout theorem. Irrational roots
 Proof of identities related with highdegree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
 Proof of identities related with highdegree expressions. High degrees. Grouping method
 Proof of identities related with highdegree expressions. High degrees. Perfect square
 Proof of identities related with highdegree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
 Proof of identities related with highdegree expressions. High degrees. Formulas of short multiplication
 Proof of identities related with highdegree expressions. High degrees. Difference of squares
 Proof of identities related with highdegree expressions. High degrees. Factorization of quadratic trinomial
 Proof of identities related with highdegree expressions. High degrees. Properties of fractions
 Proof of identities related with highdegree expressions. High degrees. Difference and sum of cubes
 Proof of identities related with highdegree expressions. High degrees. Method of substitution

Proof of identities related with fractional algebraic expressions

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

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