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

Asymptotes are two, one horizontal $x - 3 = 0$ and another slanting $y = x - 2$.
Vertical asymptotes can be found by identifying zeros of the denominator, which is $x - 3$. As such $x - 3 = 0$ is the only vertical asymptote.
As the degree of numerator is $1$ greater than degree of denominator, there is no vertical asymptote. However, as it is greater by only one degree and numerator and rational expression $\frac{{x}^{2} - 5 x + 6}{x - 3} = x - 2$, there is a slanting asymptote $y = x - 2$