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

Dec 31, 2015

#### Answer:

$x = 0$

#### Explanation:

In a rational function such as this, vertical asymptotes occur when the denominator is equal to $0$.

Set the denominator equal to $0$.

${e}^{x} - {e}^{2 x} = 0$

${e}^{x} = {e}^{2 x}$

$x = 2 x$

$x = 0$

The vertical asymptote occurs when $x = 0$. Check a graph:

graph{(e^x)/(e^x-e^(2x)) [-14.24, 14.24, -7.12, 7.12]}