Consider the function $f(x)=\frac{x^2-9}{x(x-3)}$

a$.$ Evaluate $\underset{x}{lim}f(x)$ and $\underset{x-}{lim}f(x),$ and then identify the horizontal asymptotes.

b$.$ Find the vertical asymptotes. For each vertical asymptote $x=a,$ evaluate $\underset{x{a}^{-}}{lim}f(x)$ and $\underset{x{a}^{+}}{lim}f(x).$