Find the horizontal and vertical asymptote(s) of $LaTeX: \displaystyle f(x) = \frac{x^{2} - 7 x + 6}{6 x^{2} - 6 x - 72}$ , 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 $LaTeX: \displaystyle y=\frac{1}{6}$ . The vertical asymptotes are the zeros of the denominator. $LaTeX: \displaystyle 6 x^{2} - 6 x - 72=0 \iff 6 \left(x - 4\right) \left(x + 3\right)=0$ . The vertical asymptotes are $LaTeX: \displaystyle x=-3$ and $LaTeX: \displaystyle x=4$ .