Question

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

Answer 1

Asymptotes are two, one horizontal `x-3=0` and another slanting `y=x-2`.

Explanation:

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 `(x^2-5x+6)/(x-3)=x-2`, there is a slanting asymptote `y=x-2`