Answer
$\frac{(a+4)(a-3)}{(a+3)(a+5)}$
Work Step by Step
Given : $\frac{a}{a+3}-\frac{4}{a+5}$
This becomes : $\frac{a(a+5)}{(a+3)(a+5)} - \frac{4(a+3)}{(a+3)(a+5)}$
(Finding the least common denominator)
$= \frac{a(a+5)-4(a+3)}{(a+3)(a+5)}$
$= \frac{a^{2}+5a-4a-12}{(a+3)(a+5)}$
$= \frac{a^{2}+a-12}{(a+3)(a+5)}$
$= \frac{(a+4)(a-3)}{(a+3)(a+5)}$
