Answer
There is a vertical asymptote at $x = 3$.
There is a hole at $x = -3$.
Work Step by Step
Vertical asymptotes occur where the denominator becomes undefined, which means where the denominator equals $0$.
To find vertical asymptotes, set each factor in the denominator equal to $0$:
First factor:
$x - 3 = 0$
Add $3$ to each side of the equation:
$x = 3$
Second factor:
$x + 3 = 0$
Subtract $3$ from each side of the equation:
$x = -3$
There are vertical asymptotes at $x = 3$ and $x = -3$ only if they are not zeros of the numerator as well.
In this exercise, $x = -3$ is not a vertical asymptote of the function because it is a zero for both the numerator and denominator; however, this means that there is a hole at $x = -3$.
For this function, $x = 3$ is a vertical asymptote because it is a zero only of the denominator.
