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