Question

У кого есть сердце ♥, помогите! ​

Answer 1

Ответ:

$-\frac{2}{x+5}$

Объяснение:

$1) \frac{x}{x^2-25}-\frac{x-8}{x^2-10x+25}=\frac{x}{(x-5)(x+5)}-\frac{x-8}{(x-5)^2}=\frac{x}{(x-5)(x+5)}-\frac{x-8}{(x-5)(x-5)}=\frac{x(x-5)}{(x-5)(x-5)(x+5)}-\frac{(x-8)(x+5)}{(x-5)(x-5)(x+5)}=\frac{x(x-5)-(x-8)(x+5)}{(x-5)^2(x+5)}=\frac{x^2-5x-(x^2-8x+5x-40)}{(x-5)^2(x+5)}=\frac{x^2-5x-x^2+8x-5x+40}{(x-5)^2(x+5)}=\frac{40-2x}{(x-5)^2(x+5)}=\frac{2(20-x)}{(x-5)^2(x+5)}=\frac{-2(x-20)}{(x-5)^2(x+5)}$

$2) \frac{-2(x-20)}{(x-5)^2(x+5)}:\frac{x-20}{(x-5)^2}=\frac{-2(x-20)}{(x-5)^2(x+5)}*\frac{(x-5)^2}{x-20}=\frac{-2(x-20)(x-5)^2}{(x-5)^2(x+5)(x-20)}=\frac{-2(x-20)}{(x+5)(x-20)}=\frac{-2}{x+5}=-\frac{2}{x+5}$