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

1 Answer
Shwetank Mauria
Feb 19, 2016

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#

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