Answer
$\frac{10x+12}{(x+4)(x-3)}$
Work Step by Step
By inspection, we see that the LCM of the denominators is $(x+4)(x-3)$. Therefore, we create a common denominator using this LCM and obtain:
$\frac{4}{x+4}+\frac{6}{x-3}$
=$\frac{4(x-3)+6(x+4)}{(x+4)(x-3)}$
=$\frac{4x-12+6x+24}{(x+4)(x-3)}$
=$\frac{10x+12}{(x+4)(x-3)}$
