Intermediate Algebra (6th Edition)

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

Chapter 9 - Cumulative Review: 14c

Answer

$\dfrac{y+x}{x^2y^2}$

Work Step by Step

The expression $ \dfrac{x^{-1}+y^{-1}}{xy} $ simplifies to \begin{array}{l} \dfrac{\dfrac{1}{x}+\dfrac{1}{y}}{xy} \\\\= \dfrac{\dfrac{1(y)+1(x)}{xy}}{xy} \\\\= \dfrac{\dfrac{y+x}{xy}}{xy} \\\\= \dfrac{y+x}{xy}\div xy \\\\= \dfrac{y+x}{xy}\cdot\dfrac{1}{xy} \\\\= \dfrac{y+x}{x^2y^2} .\end{array}
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