Question

Упростите выражение: 2/a-4 - a+4/a^2-6a+9 : a^2-16/2a-6

Answer 1

Объяснение:

$\frac{2}{a-4}-\frac{a+4}{a^2-6a+9}:\frac{a^2-16}{2a-6} = \frac{2}{a-4}-\frac{a+4}{(a-3)^2}:\frac{(a-4)*(a+4)}{2*(a-3)} =\frac{2}{a-4}-\frac{(a+4)*2*(a-3)}{(a-3)^2*(a-4)*(a+4)}=\\ =\frac{2}{a-4}-\frac{2}{(a-3)*(a-4)}=\frac{2*(a-3)-2}{(a-3)*(a-4)}=\frac{2a-6-2}{(a-3)*(a-4)}=\frac{2a-8}{(a-3)*(a-4)}=\\ =\frac{2*(a-4)}{(a-3)*(a-4)}= \frac{2}{a-3}.$