Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - P.5 - Rational Expressions - Exercises - Page 49: 56

Answer

$\frac{-2x^2-10x}{(x-5)^4}=\frac{-2(x^2+5x)}{(x-5)^4}$

Work Step by Step

$2x(x-5)^{-3}-4x^2(x-5)^{-4}=(x-5)^{-4}[2x(x-5)^{-3-(-4)}-4x^2]=\frac{2x(x-5)^1-4x^2}{(x-5)^4}=\frac{2x^2-10x-4x^2}{(x-5)^4}=\frac{-2x^2-10x}{(x-5)^4}=\frac{-2(x^2+5x)}{(x-5)^4}$
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