Question

Simplify:

$\left[\frac{x+y}{x^{-1}+y^{-1}}\right]-xy$

Answer 1

Given: $\frac{x+y}{x^{-1}+y^{-1}}-xy$

$=\frac{x+y}{\frac{1}{x}+\frac{1}{y}}-xy$

$=\frac{xy(x+y)}{x+y}-xy$

$=xy-xy=0$