Find the oblique (slant) asymptote of $LaTeX: \displaystyle f(x) = \frac{x^{2} - 2 x - 3}{x - 5}$ .

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 $LaTeX: \displaystyle 12$ . The oblique asymptote is $LaTeX: \displaystyle y = x + 3$ .