Answer
Domain: $(-\infty,-3)\cup(-3,1)\cup(1,\infty)$
See graph.
Work Step by Step
Step 1. Factor the function as $f(x)=\frac{(x+1)}{(x+3)(x-1)}$; there are no common factors.
Step 2. The domain requirement is that the denominator can not be zero, which gives $x\ne-3,1$. Thus the domain can be written as:
$(-\infty,-3)\cup(-3,1)\cup(1,\infty)$
Step 3. We can identify vertical asymptotes as $x=-3$ and $x=1$
Step 4. See graph.
