Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set: 38

Answer

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

Work Step by Step

$\dfrac{\dfrac{2}{x}+\dfrac{x}{2}}{\dfrac{2}{x}-\dfrac{x}{2}}$ Evaluate the sum indicated in the numerator and the substraction indicated in the denominator: $\dfrac{\dfrac{2}{x}+\dfrac{x}{2}}{\dfrac{2}{x}-\dfrac{x}{2}}=\dfrac{\dfrac{4+x^{2}}{2x}}{\dfrac{4-x^{2}}{2x}}=...$ Evaluate the division and simplify: $...=\dfrac{4+x^{2}}{2x}\div\dfrac{4-x^{2}}{2x}=\dfrac{2x(4+x^{2})}{2x(4-x^{2})}=\dfrac{4+x^{2}}{4-x^{2}}=...$ Factor the denominator to provide a more simplified answer: $...=\dfrac{x^{2}+4}{(4-x)(4+x)}$
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