Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.5 Rational Expressions - R.5 Exercises: 39

Answer

$\color{blue}{\dfrac{a+4}{a-3}}$

Work Step by Step

Use the rule $\dfrac{a}{b} \div \dfrac{c}{d}= \dfrac{a}{b} \cdot \dfrac{d}{c}$ to obtain: $=\dfrac{4a+12}{2a-10} \cdot \dfrac{a^2-a-20}{a^2-9}$ Factor each polynomial, then cancel common factors to obtain: $\require{cancel} =\dfrac{4(a+3)}{2(a-5)} \cdot \dfrac{(a-5)(a+4)}{(a-3)(a+3)} \\=\dfrac{\cancel{4}2\cancel{(a+3)}}{\cancel{2}\cancel{\cancel{(a-5)}}} \cdot \dfrac{\cancel{(a-5)}(a+4)}{(a-3)\cancel{(a+3)}} \\=\color{blue}{\dfrac{a+4}{a-3}}$
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