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

Jan 2, 2016

$x \approx 1.04991$

#### Explanation:

A vertical asymptote in a rational function will occur when the denominator is equal to $0$. Set the denominator equal to $0$ and solve for $x$.

$x {e}^{x} - 3 = 0$

This cannot be solved analytically. I recommend graphing the function and tracing the zero.

graph{xe^x-3 [-10, 10, -5, 5]}

Since $x \approx 1.04991$, that is the spot where there is a vertical asymptote.

graph{x/(xe^x-3) [-10, 10, -5, 5]}