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

Vertical asymptotes would be given by the equation $\frac{1}{x} - {e}^{x} = 0$ on solving for x.
Write f(x) = 1/ ((e^x -xe^2x)/x. Vertical asymptotes would be given by $\frac{{e}^{x} - x {e}^{2 x}}{x} = 0$
${e}^{x} \left(\frac{1}{x} - {e}^{x}\right) = 0$
Solving $\frac{1}{x} - {e}^{x} = 0$ would give vertical asymptotes