Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.5 - Integrated Review - Summary on Rational Expressions - Page 527: 17


$ \dfrac{3x^2+5x+3}{(3x-1)^2}$

Work Step by Step

$\dfrac{x+2}{3x-1}+\dfrac{5}{(3x-1)^2}$ is a rational expression $\dfrac{x+2}{3x-1}+\dfrac{5}{(3x-1)^2} = \dfrac{(x+2)(3x-1)^2+5(3x-1)}{(3x-1)(3x-1)^2} = \dfrac{(3x-1)[(x+2)(3x-1)+5]}{(3x-1)(3x-1)^2} = \dfrac{(x+2)(3x-1)+5}{(3x-1)^2} = \dfrac{3x^2-x+6x-2+5}{(3x-1)^2} = \dfrac{3x^2+5x+3}{(3x-1)^2}$
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