Помогите упростить выражение (y/x-y + x/x+y) : (1/x^2 + 1/ y^2) - y^4/ x^2-y^2

Question

Помогите упростить выражение (y/x-y + x/x+y) : (1/x^2 + 1/ y^2) - y^4/ x^2-y^2

Answer 1

(y/x-y + x/x+y) : (1/x^2 + 1/ y^2) - y^4/ x^2-y^2 = (y(x+y)+x(x-y)/(x-y)(x+y))/(x^2+y^2/x^2y^2)-y^4/(x-y)(x+y) = (xy+y^2+x^2-xy/(x-y)(x+y))/(x^2+y^2/x^2y^2)-y^4(x-y)(x+y) = (x^2+y^2/(x-y)(x+y))/(x^2+y^2/x^2y^2)-y^4(x-y)(x+y) = (x^2+y^2)(x^2y^2)/(x^2+y^2)(x-y)(x+y)-y^4/(x-y)(x+y) = x^2y^2/(x-y)(x+y)-y^4/(x-y)(x+y) = x^2y^2-y^4/(x-y)(x+y) = y^2(x^2-y^2)/(x-y)(x+y) = y^2(x-y)(x+y)/(x-y)(x+y) = y^2   

Answer 2

((х+у+х-у)/(x^2-y^2))/(x/( x^2-y^2)) = (2x/(x^2-y^2))* ((x^2-y^2)/x) = x