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: 44

Answer

$\dfrac{x}{x^{2}-4}-\dfrac{5}{x^{2}-4x+4}=\dfrac{x^{2}-7x-10}{(x-2)^{2}(x+2)}$

Work Step by Step

$\dfrac{x}{x^{2}-4}-\dfrac{5}{x^{2}-4x+4}$ Factor both rational expressions completely: $\dfrac{x}{x^{2}-4}-\dfrac{5}{x^{2}-4x+4}=\dfrac{x}{(x-2)(x+2)}-\dfrac{5}{(x-2)^{2}}=...$ Evaluate the substraction of the two rational expressions and simplify: $...=\dfrac{x(x-2)-5(x+2)}{(x-2)^{2}(x+2)}=\dfrac{x^{2}-2x-5x-10}{(x-2)^{2}(x+2)}=...$ $...=\dfrac{x^{2}-7x-10}{(x-2)^{2}(x+2)}$
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