# How do you find the slant asymptote of {-9 x^3 - 9 x^2 + 28 x + 9 }/{3 x^2 + 6 x + 2}?

Jul 29, 2016

$y = - 3 x + 3$

#### Explanation:

We can long divide the coefficients like this:

to find that:

$\frac{- 9 {x}^{3} - 9 {x}^{2} + 28 x + 9}{3 {x}^{2} + 6 x + 2} = - 3 x + 3 + \frac{16 x + 3}{3 {x}^{2} + 6 x + 2}$

So the slant asymptote is:

$y = - 3 x + 3$