College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 48: 60

Answer

$\dfrac{p(p+8)}{(2p+1)(p-5)(3p-2)}$

Work Step by Step

The factored form of the given expression, $ \dfrac{p}{2p^2-9p-5}-\dfrac{2p}{6p^2-p-2} ,$ is \begin{array}{l}\require{cancel} \dfrac{p}{(2p+1)(p-5)}-\dfrac{2p}{(2p+1)(3p-2)} .\end{array} Using the $LCD= (2p+1)(p-5)(3p-2) ,$ the expression, $ \dfrac{p}{(2p+1)(p-5)}-\dfrac{2p}{(2p+1)(3p-2)} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{(3p-2)(p)-(p-5)(2p)}{(2p+1)(p-5)(3p-2)} \\\\= \dfrac{3p^2-2p-2p^2+10p}{(2p+1)(p-5)(3p-2)} \\\\= \dfrac{p^2+8p}{(2p+1)(p-5)(3p-2)} \\\\= \dfrac{p(p+8)}{(2p+1)(p-5)(3p-2)} .\end{array}
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