Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - 7.2 - Multiplying and Dividing Algebraic Fractions - Problem Set 7.2 - Page 286: 22



Work Step by Step

We factor the expression in the numerator of the second fraction by using the rule $a^{2}-b^{2}=(a+b)(a-b)$. Then, we multiply fractions by multiplying the numerators of the fractions by each other and the denominators of the fractions by each other. Then, we cancel out the resultant common factors in the numerator and the denominator of the two fractions to simplify: $\frac{x^{2}-9}{6}\times\frac{8}{x-3}$ =$\frac{x^{2}-3^{2}}{6}\times\frac{8}{x-3}$ =$\frac{(x+3)(x-3)}{6}\times\frac{8}{x-3}$ =$\frac{(x+3)}{6}\times\frac{8}{1}$ =$\frac{(x+3)}{3}\times\frac{4}{1}$ =$\frac{4(x+3)}{3}$
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