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

The function

If we write the function as:

Analysing the limit:

Since

So the function does not have vertical asymptotes.

graph{x/(e^x-e^(2x)) [-10, 10, -5, 5]}

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The function f(x) = x/(e^x-e^(2x)) has vertical asymptotes at x = 0 and x = ln(2).

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