Answer
$(-\infty,0)\cup(0,\infty)$
Work Step by Step
We are given the function:
$f(x)=\dfrac{e^x}{x}$
The function in the numerator is an exponential function, therefore continuous.
The function in the denominator is polynomial, therefore also continuous.
Because $f$ is a rational function, it is continuous for all $x$ except those values for which the denominator is zero. Therefore the domain of $f$ is:
$D=(-\infty,0)\cup(0,\infty)$
The domain on which $f$ is continuous is:
$(-\infty,0)\cup(0,\infty)$
