Answer
Vertical asymptote: $\quad x = -3$
Hole/removable discontinuity: $\quad x = 4$
Work Step by Step
To find the vertical asymptote, find the zeros of the denominator by setting each factor equal to zero and solving:
$x + 3 = 0$
$x = -3$
Second factor:
$x - 4 = 0$
$x = 4$
We have vertical asymptotes at $x = -3$ and $x = 4$ only if they are not zeros of the numerator. In this exercise, $x = 4$ 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 removable discontinuity or hole at $x = 4$.
For this function, $x = -3$ is a vertical asymptote because it is a zero only of the denominator.
