Question

Simplify : $xy\left[\right(x+y)(\frac{1}{x}+\frac{1}{y})-2]$

Answer 1

$xy[(x+y)(\frac{1}{x}+\frac{1}{y})-2]$

$=xy[(x+y)\left(\frac{y+x}{xy}\right)-2]$

$=xy[\frac{(x+y{)}^2}{xy}-2]$

$=xy\times \frac{(x+y{)}^2}{xy}-xy\times 2$

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

$=x^2+y^2+2xy-2xy$

$=x^2+y^2$