# What are the asymptote(s) and hole(s), if any, of  f(x) =(1+1/x)/((x-3)*x)?

May 20, 2018

No holes, $x = 0 \mathmr{and} x = 3$ are the asymptotes.

#### Explanation:

There are no factors that cancel out in the numerator and denominator so there are no holes.

To find the asymptotes we set the denominator equal to 0 and solve for where the function is undefined.

$\left(x - 3\right) \cdot x = 0$

$x = 0 \mathmr{and} x = 3$ are the asymptotes.