Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 43

Answer

$\dfrac{a^{2}+7a+12}{a^{2}+5a+6}\cdot\dfrac{a^{2}+8a+15}{a^{2}+5a+4}=\dfrac{(a+3)(a+5)}{(a+1)(a+2)}$

Work Step by Step

$\dfrac{a^{2}+7a+12}{a^{2}+5a+6}\cdot\dfrac{a^{2}+8a+15}{a^{2}+5a+4}$ Factor both rational expressions completely: $\dfrac{a^{2}+7a+12}{a^{2}+5a+6}\cdot\dfrac{a^{2}+8a+15}{a^{2}+5a+4}=\dfrac{(a+4)(a+3)}{(a+3)(a+2)}\cdot\dfrac{(a+5)(a+3)}{(a+4)(a+1)}$ Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator: $...=\dfrac{(a+4)(a+3)^{2}(a+5)}{(a+1)(a+2)(a+3)(a+4)}=\dfrac{(a+3)(a+5)}{(a+1)(a+2)}$
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