Verified Answer :

\(\frac{x + 4}{ x^{2} + 5x + 6 }\) + \(\frac{x + 3}{ x^{2} - 16}\) Factor the denominator terms

\(\frac{(x + 4)(x + 3)}{(x + 3)(x + 2)(x + 4)(x - 4)}\) (x + 4) and (x + 3) will cancel out

\(\frac{1}{(x + 2)(x - 4)}\)   Here's the final answer.