Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 8.1 - 1 Rational Expressions and Functions Chapter 8.

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 8.1 - 1

Rational Expressions and Functions

Chapter 8

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 2

8.1 Rational Expressions and Functions; Multiplying and Dividing

Defining Rational Expressions

In Section 1.1, we defined rational numbers to be the quotient of two integers, a / b with b not equal to 0.

A rational expression (algebraic fraction) is the quotient of two polynomials, also with the denominator not 0. Rational expressions are the elements of the set

Examples:

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 3

8.1 Rational Expressions and Functions; Multiplying and Dividing

Define Rational Functions and Describe Their Domain

A rational function has the form

The domain of a rational function includes all the real numbers except those that make Q(x), the denominator, equal to 0.

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8.1 Rational Expressions and Functions; Multiplying and Dividing

Writing Rational Expressions in Lowest Terms

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8.1 Rational Expressions and Functions; Multiplying and Dividing

Writing Rational Expressions in Lowest Terms

3

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 6

8.1 Rational Expressions and Functions; Multiplying and Dividing

Multiplying Rational Expressions

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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 7

8.1 Rational Expressions and Functions; Multiplying and Dividing

Finding the Reciprocal of a Rational Expression

3To find the reciprocal, simply interchange the numerator and denominator.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 8

8.1 Rational Expressions and Functions; Multiplying and Dividing

Dividing Rational Expressions

3