# For what values of x, if any, does f(x) = 1/((x+8)(x-7))  have vertical asymptotes?

Jul 30, 2018

$\text{vertical asymptotes at "x=-8" and } x = 7$

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.

$\text{solve } \left(x + 8\right) \left(x - 7\right) = 0$

$x = - 8 \text{ and "x=7" are the asymptotes}$
graph{1/((x+8)(x-7) [-10, 10, -5, 5]}