Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises: 17

Answer

$= \frac{(m+3)}{(m+2)} $

Work Step by Step

$\frac{m^{2}+8m+7}{m^{2}-2m-3} \times \frac{m^{2}-9}{m^{2}+9m+14}$ $= \frac{m^{2}+7m+m+7}{m^{2}-3m+m-3} \times \frac{(m-3)(m+3)}{m^{2}+7m+2m+14}$ $= \frac{m(m+7)+1(m+7)}{m(m-3)+1(m-3)} \times \frac{(m-3)(m+3)}{m(m+7)+2(m+7)}$ $= \frac{(m+1)(m+7)}{(m+1)(m-3)} \times \frac{(m-3)(m+3)}{(m+2)(m+7)}$ $= \frac{(m+7)}{(m-3)} \times \frac{(m-3)(m+3)}{(m+2)(m+7)}$ $= \frac{(m-3)(m+3)}{(m-3)(m+2)} $ $= \frac{(m+3)}{(m+2)} $
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