Решите номер 30.Есть вложение.

Решите задачу:

$\frac{x}{x^2+y^2} - \frac{y(x-y)^2}{x^4-y^4}= \frac{x(x^2-y^2)}{(x^2+y^2)(x^2-y^2)} - \frac{y(x^2-2xy+y^2)}{(x^2-y^2)(x^2+y^2)}= \\\ = \frac{x^3-xy^2-x^2y+2xy^2-y^3}{(x^2+y^2)(x^2-y^2)}= \frac{x^2(x-y)+y^2(x-y)}{(x^2+y^2)(x^2-y^2)}= \frac{(x-y)(x^2+y^2)}{(x^2+y^2)(x-y)(x+y)}=\frac{1}{x+y}$

$\frac{b(a+b)^2}{a^4-b^4} + \frac{a}{a^2+b^2} = \frac{b(a^2+2ab+b^2)}{(a^2-b^2)(a^2+b^2)} + \frac{a(a^2-b^2)}{(a^2+b^2)(a^2-b^2)} = \\\ =\frac{a^2b+2ab^2+b^3+a^3-ab^2}{(a^2-b^2)(a^2+b^2)}=\frac{a^2(a+b)+b^2(a+b)}{(a^2-b^2)(a^2+b^2)}=\frac{(a+b)(a^2+b^2)}{(a-b)(a+b)(a^2+b^2)}=\frac{1}{a-b}$