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: 80

Answer

$\frac{-2x}{(x+6)^4}$

Work Step by Step

We factor out $(x+6)$ and cancel with the denominator. Then we simplify: $\displaystyle \frac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\frac{(x+6)^{3}[2x(x+6)-4x^{2}]}{(x+6)^{8}}=\frac{2x^{2}+12x-4x^{2}}{(x+6)^{5}}=\frac{12x-2x^{2}}{(x+6)^{5}}=\frac{2x(6-x)}{(x+6)^{5}}=\frac{-2x}{(x+6)^4}$
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