Answer
Vertical asymptotes are $x=0\,;\ x=-4$ and there are no holes.
Work Step by Step
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 function $f\left( x \right)$ if $x=a$ is a zero of the denominator $q\left( x \right)$.
Equate the denominator to zero.
$\begin{align}
& x\left( x+4 \right)=0 \\
& x=0\ \text{or }x+4=0 \\
& x=0\ \text{or }x=-4 \\
\end{align}$
Thus, $x=0\text{ and }x=-4$ 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 a numerator and $q\left( x \right)$ is a 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 $x+3$ and $x\left( x+4 \right)$. So, there is are holes.
Hence, $x=0\,;\ x=-4$ is a vertical asymptote and there are no holes.
