Question

ДОВЕДІТЬ ТОТОЖНІСТЬ! Завдання на фото даю 40балів

Answer 1

Ответ:

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

Объяснение:

$\displaystyle \frac{4+x}{x^2+9-6x}:\frac{x^2-16}{2x-6}-\frac{2}{x-4}=\\\\\\\frac{x+4}{(x-3)^2}:\frac{(x-4)(x+4)}{2(x-3)}-\frac{2}{x-4}=\\\\\\\frac{x+4}{(x-3)^2}\cdot \frac{2(x-3)}{(x-4)(x+4)}-\frac{2}{x-4}=\\\\\\\frac{1}{x-3}\cdot \frac{2}{x-4}-\frac{2}{x-4}=\\\\\\\frac{2}{(x-3)(x-4)}-\frac{2}{x-4}=$

$\displaystyle \frac{2}{(x-3)(x-4)}-\frac{2(x-3)}{(x-3)(x-4)}=\\\\\\\frac{2-2(x-3)}{(x-3)(x-4)}=\frac{2-2x+6}{(x-3)(x-4)}=\\\\\\\frac{-2x+8}{(x-3)(x-4)}=\frac{-2(x-4)}{(x-3)(x-4)}=\\\\\\\frac{-2}{x-3}=\frac{2}{3-x}$