#### Answer

$\frac{1}{x-4}$

#### Work Step by Step

To simplify, divide both the numerator and denominator by their greatest common factor.
Use the factorization to find the GCF.
$\frac{x+4}{x^2-16}=\frac{(x+4)}{(x+4)(x-4)}=\frac{(x+4)\div(x+4)}{(x+4)(x-4)\div(x+4)}=\frac{1}{x-4}$