Answer
$a=6$
Work Step by Step
We simplify as follows:
$\frac{-4}{a^{2}+2a-8}+\frac{1}{a^{2}+9a+20}=\frac{-4}{a^{2}+3a-10}$
$\frac{-4}{(a+4)(a-2)}+\frac{1}{(a+5)(a+4)}=\frac{-4}{(a-2)(a+5)}$
$\frac{-4(a+5)}{(a-2)(a+4)(a+5)}+\frac{a-2}{(a-2)(a+4)(a+5)}=\frac{-4(a+4)}{(a-2)(a+4)(a+5)}$
$\frac{-4a-20}{(a-2)(a+4)(a+5)}+\frac{a-2}{(a-2)(a+4)(a+5)}=\frac{-4a-16}{(a-2)(a+4)(a+5)}$
$-4a-20+a-2=-4a-16$
$-3a-22=-4a-16$
$a=6$
