Question

Solve
$xy\left[\right(x+y\left)\right(\frac{1}{x}+\frac{1}{y})-y]=(x-y{)}^2$

Answer 1

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

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

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

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

$4xy-x{y}^2=0$

$xy(4-y)=0$

$xy=0,y=4$