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: 76

Answer

$\dfrac{5}{x-2}+\dfrac{7x}{x^{2}-4}-\dfrac{11}{x}=\dfrac{x^{2}+10x+44}{x(x-2)(x+2)}$

Work Step by Step

$\dfrac{5}{x-2}+\dfrac{7x}{x^{2}-4}-\dfrac{11}{x}$ Factor the denominator of the second fraction: $\dfrac{5}{x-2}+\dfrac{7x}{x^{2}-4}-\dfrac{11}{x}=\dfrac{5}{x-2}+\dfrac{7x}{(x-2)(x+2)}-\dfrac{11}{x}=...$ Evaluate the indicated operations and simplify: $...=\dfrac{5x(x+2)+7x(x)-11(x-2)(x+2)}{x(x-2)(x+2)}=...$ $...=\dfrac{5x^{2}+10x+7x^{2}-11x^{2}+44}{x(x-2)(x+2)}=\dfrac{x^{2}+10x+44}{x(x-2)(x+2)}$
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