Question

Solve:

$\frac{a^2+5a+6}{a^2-a-12}\times \frac{a-4}{a^2-4}$

Answer 1

Given,

$\Rightarrow \frac{a^2+5a+6}{a^2-a-12}\times \frac{a-4}{a^2-4}$

$=\frac{a^2+3a+2a+6}{a^2-4a+3a-12}\times \frac{a-4}{(a+2)(a-2)}$

$=\frac{a(a+3)+2(a+3)}{a(a-4)+3(a-3)}\times \frac{(a-4)}{(a+2)(a-2)}$

$=\frac{(a+3)(a+2)}{(a-4)(a+3)}\times \frac{(a-4)}{(a+2)(a-2)}$

$=\frac{1}{a-2}$.