Section 12 2 Multiplying and Dividing Rational Expressions

Section 12. 2 Multiplying and Dividing Rational Expressions Copyright © 2011 Pearson Education, Inc.

Multiplying and Dividing Rational Expressions Property of Multiplication of Rational Function Property If and are rational expressions and B and D are nonzero, then In words: To multiply two rational expressions, write the numerators as a product and write the denominator as a product. Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 2

Multiplying and Dividing Rational Expressions Multiply Rational Expressions Example Find the product . Simplify the result. Solution Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 3

Multiplying and Dividing Rational Expressions Multiply Rational Expressions Example Find the product . Simplify the result. Solution Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 4

Multiplying and Dividing Rational Expressions Multiply Rational Expressions Process To multiply two rational expressions, 1. Factor the numerators and the denominators. 2. Multiply by using the property , where B and D are nonzero. 3. Simplify the result. Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 5

Multiplying and Dividing Rational Expressions Finding a Product Function Example Let and 1. Find an equation of the product function 2. Find Solution Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 6

Multiplying and Dividing Rational Expressions Finding a Product Function Solution Example Continued Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 7

Division of Rational Expressions Property of Dividing Rational Expressions Property If and are rational expressions and B, C, and D are nonzero, then In words: To divide by a rational expression, multiply by its reciprocal. Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 8

Division of Rational Expressions Property of Dividing Rational Expressions Example Find the quotient Solution Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 9

Division of Rational Expressions Property of Dividing Rational Expressions Solution Continued Example Process To divide two rational expressions, 1. Write the quotient as a product by using property: , where B, C, and D are nonzero. 2. Find the product. 3. Simplify. Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 10

Division of Rational Expressions Dividing Two Rational Expressions Example Find the quotient Solution Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 11

Division of Rational Expressions Dividing Two Rational Expressions Solution Continued Example Let 1. Find an equation of the quotient function. 2. Find Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 12

Division of Rational Expressions Finding a Quotient Function Solution Find the quotient Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 13

Division of Rational Expressions Finding a Quotient Function Solution Continued Find the quotient Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 14

Division of Rational Expressions Combining Three Rational Equations Example Perform the indicated operations: Solution Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 15

Division of Rational Expressions Combining Three Rational Equations Solution Example Continued Copyright © 2011 Pearson Education, Inc. Section 12. 2 Lehmann, Elementary and Intermediate Algebra, 1 ed Slide 16