Find the horizontal and vertical asymptote(s) of $LaTeX: \displaystyle f(x) = \frac{x^{2} + 20 x + 99}{3 x^{2} - 9 x - 30}$ , if they exist.

The degree of the numerator is the same as the degree of the denominator, so the horizontal asymptote is the ratio of the leading coefficients $LaTeX: \displaystyle y=\frac{1}{3}$ . The vertical asymptotes are the zeros of the denominator. $LaTeX: \displaystyle 3 x^{2} - 9 x - 30=0 \iff 3 \left(x - 5\right) \left(x + 2\right)=0$ . The vertical asymptotes are $LaTeX: \displaystyle x=-2$ and $LaTeX: \displaystyle x=5$ .