# How do you find the slant asymptote of f(x) = (2x^2 + 3x + 8)/(x + 3)?

May 14, 2018

y = 2x-3

#### Explanation:

Use polynomial long division:

Thus $\setminus \frac{2 {x}^{2} + 3 x + 8}{x + 3} = 2 x - 3 + \setminus \frac{17}{x + 3}$
$\setminus {\lim}_{x \setminus \to \setminus \infty} \left[2 x - 3 + \setminus \frac{17}{x + 3}\right] = 2 x - 3$
$\setminus {\lim}_{x \setminus \to - \setminus \infty} \left[2 x - 3 + \setminus \frac{17}{x + 3}\right] = 2 x - 3$

Thus the obliques asymptote is $y = 2 x - 3$