jmc

After factoring the denominator, we get $f(x)=\frac{x+2}{(x-6)(x+4)}$. The domain of a rational function is the set of all real numbers, except for those at which the function is undefined, which is where our denominator equals 0. The denominator equals 0 when $x=6$ or $x=-4$, which means that the domain is $x\in \boxed{(-\infty ,-4)\cup (-4,6)\cup (6,\infty )}$.