Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 40

Answer

$\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}=-\dfrac{x}{x-1}$

Work Step by Step

$\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}$ Factor the denominator of the first fraction and simplify only the first fraction: $\dfrac{x-1}{x^{2}-2x+1}-\dfrac{x+1}{x-1}=\dfrac{x-1}{(x-1)^{2}}-\dfrac{x+1}{x-1}=...$ $...=\dfrac{1}{x-1}-\dfrac{x+1}{x-1}=...$ Evaluate the substraction and simplify if possible: $...=\dfrac{1-x-1}{x-1}=-\dfrac{x}{x-1}$
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