# For what values of x, if any, does f(x) = e^x/(e^x-3e^x)  have vertical asymptotes?

Dec 20, 2016

$f \left(x\right)$ is a constant and has no vertical asymptotes.
We can write $f \left(x\right)$ as:
$f \left(x\right) = {e}^{x} / \left({e}^{x} - 3 {e}^{x}\right) = {e}^{x} / \left(- 2 {e}^{x}\right) = - \frac{1}{2}$
So, $f \left(x\right)$ is a constant and has no vertical asymptotes.