Find the oblique (slant) asymptote of $LaTeX: \displaystyle f(x) = \frac{x^{3} - 7 x^{2} - 20 x + 96}{x^{2} - 4 x - 12}$ .

The oblique asymptote is the whole part without the remainder after polynomial long division.

Dividing gives the quotient $LaTeX: \displaystyle x - 3$ and the remainder $LaTeX: \displaystyle 60 - 20 x$ . The oblique asymptote is $LaTeX: \displaystyle y = x - 3$ .