How do you find the asymptotes for (x^2 - 5x + 6)/(x - 3)?

1 Answer
Jul 29, 2016

This function has no asymptotes. It has a hole at $\left(3 , 1\right)$.

Explanation:

$\frac{{x}^{2} - 5 x + 6}{x - 3} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 3\right)}}} \left(x - 2\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 3\right)}}}} = x - 2$

with exclusion $x \ne 3$

This is a straight line with a hole at $\left(3 , 1\right)$

It has no asymptotes.