# What are the asymptotes of (x^2 - 5x + 6)/ (x - 3)?

May 4, 2016

$y = x - 2$ where $x \ne 3$

#### Explanation:

${x}^{2} - 5 x + 6 = \left(x - 2\right) \left(x - 3\right)$

So we have: (x^2-5x+6)/(x-3) = ((x-2)cancel((x-3)))/(cancel((x-3))

So as a general equation we have $y = x - 2$

But this has a limiting factor that $\left(x - 3\right) \ne 0 \implies x \ne 3$

So 3 is an excluded value