Question

Xy{(x+y)(1/x+1/y)-4}=(x-y)2

Answer 1

$\mathrm{xy((x+y)( \frac{1}{x} + \frac{1}{y} )-4)=(x-y)2} \\\ \mathrm{xy((1+ \frac{x}{y} + \frac{y}{x} +1)-4)=(x-y)2} \\\ \mathrm{(xy+x^2+y^2+xy-4xy)=(x-y)2} \\\ \mathrm{(x^2+y^2-2xy)=(x-y)2} \\\ \mathrm{(x-y)^2=(x-y)2} \\\ \boxed{\mathrm{x-y=2}} \Leftarrow$