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

$\dfrac{x^{-1}+y^{-1}}{(x+y)^{-1}}=\dfrac{(x+y)^{2}}{xy}$

#### 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: $...=\dfrac{(x+y)(x+y)}{xy}=\dfrac{(x+y)^{2}}{xy}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.