R 5 day 2 Multiply and Divide Rational

R. 5 day 2 Multiply and Divide Rational Expressions Learning Target: You will be able to multiply and divide rational expressions, and simplify the product or quotient.

Multiply rational expressions. • The product of two fractions is found by multiplying the numerators and multiplying the denominators. Rational expressions are multiplied in the same way. • The product of the rational expressions and is • That is, to multiply rational expressions, multiply the numerators and multiply the denominators. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 2 - 3

EXAMPLE 1 Multiplying Rational Expressions • Multiply. Write each answer in lowest terms. Solution: It is also possible to divide out common factors in the numerator and denominator before multiplying the Copyright © 2008 Pearson Education, Inc. Publishing as rational expressions. Pearson Addison-Wesley Slide 7. 2 - 4

Multiply the fractions Reduce before multiply.

Multiply the fractions Reduce before multiply.

Example 2 Multiply rational expressions Step 1: Factor and Multiply

Checkpoint Multiply the expression 6 x² + 18 x x² - x – 2 x² + x – 6 * x² - 7 x – 8 6 x(x + 3)(x-2)(x+1) (x+3)(x-2)(x-8)(x+1) 6 x x-8

More Examples • Multiply the expressions. Simplify the result.

Divide rational expressions. Division of rational expressions is defined as follows. If then and are any two rational expressions with That is, to divide one rational expression by another rational expression, multiply the first rational expression by the reciprocal of the second rational expression. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 2 - 12

EXAMPLE 4 Dividing Rational Expressions • Divide. Write each answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 2 - 13

EXAMPLE 5 • Dividing Rational Expressions Divide. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 2 - 14

EXAMPLE 6 • Dividing Rational Expressions Divide. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 2 - 15

EXAMPLE 7 Dividing Rational Expressions (Factors Are Opposites) • Divide. Write in the answer in lowest terms. Solution: Remember to write − 1 when dividing out factors that are opposite of each other. It may be written in the numerator Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley or denominator, but not both. Slide 7. 2 - 16

Divide the Rational Expressions You can only Reduce when Multiplying

Example 4 Divide rational expressions Step 1: Multiply by reciprocal Step 2: Factor and Multiply Step 3: Simplify

More Examples • Divide each expression. Simplify the result.

Homework • R. 5 (pg 53) #33 -49 odd