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

2. 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:

3. 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.

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 4 8.1 Rational Expressions and Functions; Multiplying and Dividing Writing Rational Expressions in Lowest Terms 3

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 5 8.1 Rational Expressions and Functions; Multiplying and Dividing Writing Rational Expressions in Lowest Terms 3

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 6 8.1 Rational Expressions and Functions; Multiplying and Dividing Multiplying Rational Expressions 3

7. 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 3 To find the reciprocal, simply interchange the numerator and denominator.

8. 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