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

2. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 8.1 - 2 Rational Expressions and Functions Chapter 8

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

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 4 8.1 Rational Expressions and Functions; Multiplying and Dividing Objectives 1.Define rational expressions. 2.Define rational functions and describe their domains. 3.Write rational expressions in lowest terms. 4.Multiply rational expressions. 5.Find reciprocals for rational expressions. 6.Divide rational expressions.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 5 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:

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

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 7 8.1 Rational Expressions and Functions; Multiplying and Dividing Define Rational Functions and Describe Their Domain 3 3 2 The graph of the function f(x) is shown at the right. The domain of this function is all real numbers except x = 3 where f(x) is not defined.

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 8 8.1 Rational Expressions and Functions; Multiplying and Dividing Finding Numbers Not in the Domain of a Rational Function 3 To locate the values not in the domain of a rational function, we need only determine which real numbers make the denominator 0.

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 9 8.1 Rational Expressions and Functions; Multiplying and Dividing Writing Rational Expressions in Lowest Terms 3

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 10 8.1 Rational Expressions and Functions; Multiplying and Dividing Writing Rational Expressions in Lowest Terms 3

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 11 8.1 Rational Expressions and Functions; Multiplying and Dividing When the Numerator and Denominator are Opposites 3

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 12 8.1 Rational Expressions and Functions; Multiplying and Dividing Multiplying Rational Expressions 3

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 13 8.1 Rational Expressions and Functions; Multiplying and Dividing Multiplying Rational Expressions 3

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 14 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.

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 15 8.1 Rational Expressions and Functions; Multiplying and Dividing Dividing Rational Expressions 3