Question

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

Answer 1

`x~~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`.

`xe^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~~1.04991`, that is the spot where there is a vertical asymptote.

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