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: 43

Answer

$\dfrac{x(6y+x)}{2y}$

Work Step by Step

The given expression, $ \dfrac{3x^{-1}+(2y)^{-1}}{x^{-2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{3}{x^1}+\dfrac{1}{2y}}{\dfrac{1}{x^2}} \\\\= \dfrac{\dfrac{6y+x}{2xy}}{\dfrac{1}{x^2}} \\\\= \dfrac{6y+x}{2xy}\div\dfrac{1}{x^2} \\\\= \dfrac{6y+x}{2xy}\cdot x^2 \\\\= \dfrac{6y+x}{2\cancel{x}y}\cdot \cancel{x}\cdot x \\\\= \dfrac{x(6y+x)}{2y} .\end{array}
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