Question

x/x^2+y^2-y*(x-y)^2/x^4-y^4 пожалуйста помогите надо упростить

Answer 1

$\dfrac{x}{x^2+y^2}-\dfrac{y(x-y)^2}{(x^2-y^2)(x^2+y^2)}=\dfrac{x}{x^2+y^2}-\dfrac{y(x-y)^2}{(x-y)(x+y)(x^2+y^2)}=\\ \\ \\ =\dfrac{x}{x^2+y^2}-\dfrac{y(x-y)}{(x+y)(x^2+y^2)}=\dfrac{x(x+y)-y(x-y)}{(x+y)(x^2+y^2)}=\dfrac{x^2+xy-xy+y^2}{(x+y)(x^2+y^2)}=\\ \\ \\ =\dfrac{x^2+y^2}{(x+y)(x^2+y^2)}=\dfrac{1}{x+y}$