Simplify basic math expression

Question

The task is so simplify the following expression.

Thank you for any help.

Answer 1

Simplifying:

$\frac{1}{(x + y)^{2}}\big(\frac{1}{x^{2}} + \frac{1}{y^{2}}\big) + \frac{2}{(x + y)^{3}}\big(\frac{1}{x} + \frac{1}{y}\big)$,

$\frac{1}{(x+y)^{2}}\frac{x^{2} + y^{2}}{x^{2}y^{2}} + \frac{2}{(x+y)^{3}}\frac{x + y}{xy}$,

$\frac{1}{(x + y)^{2}}\frac{x^{2} + y^{2}}{x^{2}y^{2}} + \frac{2}{(x +y)^{2}xy}$,

$\frac{1}{(x+y)^{2}}\big(\frac{x^{2}+y^{2}}{x^{2}y^{2}} + \frac{2xy}{x^{2}y^{2}}\big)$,

$\frac{1}{(x+y)^{2}}\frac{(x +y)^{2}}{x^{2}y^{2}}$,

$\boxed{\frac{1}{x^{2}y^{2}}.}$