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Rational Expressions and Their Simplification
Radical Expressions and Equations
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Simplifying Algebraic Expressions
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Rational Expressions Worksheet
Adding and Subtracting Rational Expressions
Rational Expressions
Multiplying and Dividing Rational Expressions
Dividing Fractions, Mixed Numbers, and Rational Expressions
Multiplying and Dividing Rational Expressions
Multiplying and Dividing Rational Expressions
Simplifying Rational Expressions
Complex Rational Expressions
Rational Expressions and Equations
Integration of Polynomial Rational Expressions
Algebraic Expressions
Radical Expressions & Radical Functions
Rational Class and Expression Evaluator
Adding and Subtracting Rational Expressions
Rational Expressions
Radical Expressions
Multiplying Rational Expressions
Rational Expressions and Common Denominators
rational expressions
Polynomial Expressions
Rational Functions, and Multiplying and Dividing Rational Expressions
Simplifying Radical Expressions
Adding and Subtracting Rational Expressions
Rational Expressions and Equations
Rational Expressions
RATIONAL EXPRESSIONS II
Simplifying Expressions
Quadratic Expressions,Equations and Functions
RATIONAL EXPRESSIONS
Absolute Value and Radical Expressions,Equations and Functions
Rational Expressions & Functions

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Rational Expressions and Equations

Study Strategy –Preparing for a Cumulative Exam

•Preparing for a Cumulative Review
•Old Quizzes and Tests
•Homework and Notes
•Problems from Your Instructor
•Cumulative Review Exercises
•Applied Problems
•Study Groups

Section 7.1 –Rational Expressions and Functions

Concept –Rational Expressions
A rational expression is a quotient of two polynomials. The denominator of a rational expression must be nonzero, as division by zero is undefined.

Example –Rational Expressions

Concept –Values for Which a Rational Expression is Undefined

To find the values for which a rational expression is undefined, we set the denominator equal to 0 and solve the resulting equation. These solutions are the values for which the expression is undefined.

Example –Values for Which a Rational Expression is Undefined

Find the values for which the rational expression is undefined:

The expression is undefined for x=3,6.

Concept –Simplifying a Rational Expression to Lowest Terms

To simplify a rational expression to lowest terms, we first factor the numerator and denominator. Then we may divide out common factors in the numerator and denominator.

Example –Simplifying a Rational Expression to Lowest Terms

Simplify to lowest terms:

Concept –Factors That Are Opposites

Two expressions of the form a-b and b-a are opposites. The rational expression

simplifies to equal -1,as any fraction whose numerator is the opposite of its denominator is equal to -1.

Example –Factors That Are Opposites

Simplify to lowest terms:

Section 7.2 –Multiplication and Division of Rational Expressions

Concept –Multiplying Rational Expressions

To multiply two rational expressions, factor each numerator and denominator completely. Divide out factors that are common to a numerator and a denominator and multiply the remaining factors, leaving the numerator and denominator in factored form.

Example –Multiplying Rational Expressions

Concept –Dividing Rational Expressions

To divide a rational expression by another rational expression, replace the divisor by its reciprocal and then multiply.

Example –Dividing Rational Expressions