Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 43: 70



Work Step by Step

$\dfrac{x^{-1}+y^{-1}}{(x+y)^{-1}}$ Rewrite the expression: $\dfrac{x^{-1}+y^{-1}}{(x+y)^{-1}}=\dfrac{\dfrac{1}{x}+\dfrac{1}{y}}{\dfrac{1}{x+y}}=...$ Evaluate the sum in the numerator: $...=\dfrac{\dfrac{y+x}{xy}}{\dfrac{1}{x+y}}=...$ Evaluate the division: $...=\dfrac{(x+y)(x+y)}{xy}=\dfrac{(x+y)^{2}}{xy}$
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