# For what values of x, if any, does f(x) = 1/((x-2)(x+2)(e^x-1))  have vertical asymptotes?

May 31, 2016

$x = \pm 2 , x = 0$

#### Explanation:

Vertical asymptotes occur whenever the denominator of a rational function equals zero. In this case, one of the three binomials in the denominator must equal zero.

1. $\left(x - 2\right) = 0 \implies x = 2$

2. $\left(x + 2\right) = 0 \implies x = - 2$

3. $\left({e}^{x} - 1\right) = 0 \implies {e}^{x} = 1 \implies x = \ln \left(1\right) = 0$