Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set: 43

Answer

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

Work Step by Step

$\dfrac{x}{x^{2}-1}-\dfrac{2}{x^{2}-2x+1}$ Factor both rational expressions completely: $\dfrac{x}{x^{2}-1}-\dfrac{2}{x^{2}-2x+1}=\dfrac{x}{(x-1)(x+1)}-\dfrac{2}{(x-1)^{2}}=...$ Evaluate the substraction of the two rational expressions and simplify: $...=\dfrac{x(x-1)-2(x+1)}{(x+1)(x-1)^{2}}=\dfrac{x^{2}-x-2x-2}{(x+1)(x-1)^{2}}=...$ $...=\dfrac{x^{2}-3x-2}{(x+1)(x-1)^{2}}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.