Find the oblique (slant) asymptote of $LaTeX: \displaystyle f(x) = \frac{x^{3} - 10 x^{2} + 17 x - 8}{x^{2} - 6 x + 9}$ .

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

Dividing gives the quotient $LaTeX: \displaystyle x - 4$ and the remainder $LaTeX: \displaystyle 28 - 16 x$ . The oblique asymptote is $LaTeX: \displaystyle y = x - 4$ .