Question

Доведіть тотожність. Помогите пожалуйста

Answer 1

Ответ:

$\frac{4+x}{x^2+9-6x}:\frac{x^2-16}{2x-6}-\frac{2}{x-4}=\frac{2}{3-x}$

Объяснение:

$\frac{4+x}{x^2+9-6x}:\frac{x^2-16}{2x-6}-\frac{2}{x-4}=\frac{x+4}{(x-3)^2}:\frac{(x-4)(x+4)}{2(x-3)}-\frac{2}{x-4}=\\\\\frac{x+4}{(x-3)^2}\cdot\frac{2(x-3)}{(x-4)(x+4)}-\frac{2}{x-4}=\frac{2}{(x-3)(x-4)}-\frac{2}{x-4}=\\\\\frac{2}{(x-3)(x-4)}-\frac{2(x-3)}{(x-3)(x-4)}=\frac{2-2(x-3)}{(x-3)(x-4)}=\\\\\frac{2-2x+6}{(x-3)(x-4)}=\frac{-2x+8}{(x-3)(x-4)}=\\\\\frac{-2(x-4)}{(x-3)(x-4)}=\frac{-2}{x-3}=\frac{2}{3-x}$