## Precalculus (6th Edition) Blitzer

Vertical asymptote is $x=3$ and there are no holes.
If there is a rational function $f\left( x \right)=\frac{p\left( x \right)}{q\left( x \right)}$ where $p\left( x \right)$ is a numerator and $q\left( x \right)$ is a denominator then $x=a$ is a vertical asymptote of the function $f\left( x \right)$ if $x=a$ is a zero of the denominator $q\left( x \right)$. Equate the denominator to zero. \begin{align} & x-3=0 \\ & x=3 \end{align} Thus, $x=3$ is a vertical asymptote. If there is a rational function $f\left( x \right)=\frac{p\left( x \right)}{q\left( x \right)}$ where $p\left( x \right)$ is the numerator and $q\left( x \right)$ is the denominator then $x=a$ is called a hole if $x-a$ is a common factor of the numerator and denominator. There is no common factor between $x$ and $x-3$. So, there are no holes. Hence, $x=3$ is a vertical asymptote and there are no holes.