Answer
$\frac{(x+y)(x+y) }{xy}$.
Work Step by Step
The given expression is
$=\frac{x^{-1}+y^{-1}}{(x+y)^{-1}}$
Multiply the numerator and the denominator by $xy(x+y)$.
$=\frac{xy(x+y)}{xy(x+y)}\cdot \frac{x^{-1}+y^{-1}}{(x+y)^{-1}}$
Use the distributive property.
$=\frac{xy(x+y) \cdot x^{-1}+xy(x+y) \cdot y^{-1}}{xy(x+y) \cdot (x+y)^{-1}}$
Simplify.
$=\frac{x^{-1+1}y(x+y) +xy^{-1+1}(x+y) }{xy(x+y)^{-1+1}}$
$=\frac{x^{0}y(x+y) +xy^{0}(x+y) }{xy(x+y)^{0}}$
$=\frac{y(x+y) +x(x+y) }{xy}$
Factor out common terms in the numerator.
$=\frac{(x+y)(x+y) }{xy}$.
