Question

Решите номер 30.Есть вложение.

Answer 1

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

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