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

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Answer 1 · 2015-12-31T06:01:39

#x=0#

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^(2x)=0#

#e^x=e^(2x)#

#x=2x#

#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]}