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: 48

Answer

$= \frac{(7p+5)}{(3p-8)}$

Work Step by Step

$\frac{28p^{2}+41p+15}{6p^{2}+11p-72} \div \frac{4p^{2}+7p+3}{2p^{2}+11p+9}$ $= \frac{28p^{2}+41p+15}{6p^{2}+11p-72} \times \frac{2p^{2}+11p+9}{4p^{2}+7p+3}$ $= \frac{28p^{2}+20p+21p+15}{6p^{2}+27p-16p-72} \times \frac{2p^{2}+9p+2p+9}{4p^{2}+4p+3p+3}$ $= \frac{4p(7p+5)+3(7p+5)}{3p(2p+9)-8(2p+9)} \times \frac{p(2p+9)+1(2p+9)}{4p(p+1)+3(p+1)}$ $= \frac{(4p+3)(7p+5)}{(3p-8)(2p+9)} \times \frac{(p+1)(2p+9)}{(4p+3)(p+1)}$ $= \frac{(4p+3)(7p+5)}{(3p-8)} \times \frac{(p+1)}{(4p+3)(p+1)}$ $= \frac{(7p+5)}{(3p-8)} \times \frac{(p+1)}{(p+1)}$ $= \frac{(7p+5)}{(3p-8)} \times \frac{1}{1}$ $= \frac{(7p+5)}{(3p-8)} \times 1$ $= \frac{(7p+5)}{(3p-8)}$
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