Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Cumulative Review: 4

Answer

$ -\dfrac{x^2-23x-38}{(x-2)(x+2)^2}$

Work Step by Step

$\dfrac{5}{x-2}+\dfrac{3}{x^2+4x+4}-\dfrac{6}{x+2} = \dfrac{5(x+2)-6(x-2)}{(x-2)(x+2)} + \dfrac{3}{(x+2)^2} = \dfrac{(x+2)^2(5x+10-6x+12)+3(x-2)(x+2)}{(x-2)(x+2)(x+2)^2} = \dfrac{(x+2)(22-x)+3(x-2)}{(x-2)(x+2)^2} = \dfrac{22x-x^2+44-2x+3x-6}{{(x-2)(x+2)^2}} = \dfrac{-x^2+23x+38}{(x-2)(x+2)^2} = -\dfrac{x^2-23x-38}{(x-2)(x+2)^2}$
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