Answer
domain: $(-\infty,2)\cup(2,\infty)$
See graph.
Work Step by Step
Step 1. Factor the function as $f(x)=\frac{(x+3)(x-3)}{x-2}$; there are no common factors.
Step 2. The domain requirement is that the denominator can not be zero, which gives $x\ne2$. Thus the domain can be written as $(-\infty,2)\cup(2,\infty)$
Step 3. Rewrite the function as $f(x)=\frac{x^2-4-5}{x-2}=x+2-\frac{5}{x-2}$; we can find a slant asymptote as $y=x+2$
Step 4. See graph.
