College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 79

Answer

$\frac{(x+2)^{2}(x-13)}{(x-3)^{3}}$

Work Step by Step

We factor out the $(x+2)$ and $(x-3)$ terms and then simplify: $\displaystyle \frac{3(x+2)^{2}(x-3)^{2}-(x+2)^{3}(2)(x-3)}{(x-3)^{4}}=\frac{(x+2)^{2}(x-3)[3(x-3)-(x+2)(2)]}{(x-3)^{4}} =\frac{(x+2)^{2}(3x-9-2x-4)}{(x-3)^{3}}=\frac{(x+2)^{2}(x-13)}{(x-3)^{3}}$
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