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: 43

Answer

$\color{blue}{\dfrac{m+6}{m+3}}$

Work Step by Step

Use the rule $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \cdot \dfrac{d}{c}$ to obtain: $=\dfrac{m^2+3m+2}{m^2+5m+4} \cdot \dfrac{m^2+10m+24}{m^2+5m+6}$ Factor each polynomial, then cancel the common factors to obtain: $\require{cancel} \\=\dfrac{(m+1)(m+2)}{(m+1)(m+4)} \cdot \dfrac{(m+6)(m+4)}{(m+3)(m+2)} \\=\dfrac{\cancel{(m+1)}\cancel{(m+2)}}{\cancel{(m+1)}\cancel{(m+4)}} \cdot \dfrac{(m+6)\cancel{(m+4)}}{(m+3)\cancel{(m+2)}} \\=\color{blue}{\dfrac{m+6}{m+3}}$
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