Find the oblique (slant) asymptote of $LaTeX: \displaystyle f(x) = \frac{x^{3} + 8 x^{2} + 9 x - 18}{x^{2} - 8 x + 15}$ .

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

Dividing gives the quotient $LaTeX: \displaystyle x + 16$ and the remainder $LaTeX: \displaystyle 122 x - 258$ . The oblique asymptote is $LaTeX: \displaystyle y = x + 16$ .