# How do you find the slant asymptote of y = (x^2 -3x +2) / (x - 4)?

Jan 15, 2016

$y = x + 1$

#### Explanation:

$\left({x}^{2} - 3 x + 2\right) \div \left(x - 4\right) = \textcolor{g r e e n}{\left(x + 1\right)}$ plus an irrelevant constant remainder
graph{(y-(x^2-3x+2)/(x-4))(y-(x+1))=0 [-22.8, 28.53, -10.58, 15.06]}

If $y = f \frac{x}{g} \left(x\right)$ where $f \left(x\right)$ and $g \left(x\right)$ are both polynomial functions
$\textcolor{w h i t e}{\text{XXX}}$and $\text{degree"(f(x)) > "degree} \left(g \left(x\right)\right)$
then (disregarding any remainder)
$\textcolor{w h i t e}{\text{XXX}}$the oblique (or "slant") asymptote is given by the equation
color(white)("XXXXXX")y=f(x)/(g(x)