Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.3 - Simplifying Complex Fractions - Exercise Set - Page 361: 30

Answer

$\dfrac{x+4}{4}$

Work Step by Step

The given expression, $ \dfrac{\dfrac{x}{4}-\dfrac{4}{x}}{1-\dfrac{4}{x}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{x^2-16}{4x}}{\dfrac{x-4}{x}} \\\\= \dfrac{x^2-16}{4x}\div\dfrac{x-4}{x} \\\\= \dfrac{x^2-16}{4x}\cdot\dfrac{x}{x-4} \\\\= \dfrac{(x+4)(x-4)}{4x}\cdot\dfrac{x}{x-4} \\\\= \dfrac{(x+4)(\cancel{x-4})}{4\cancel{x}}\cdot\dfrac{\cancel{x}}{\cancel{x-4}} \\\\= \dfrac{x+4}{4} .\end{array}
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