Question

How do you find all the asymptotes for `(x-2)/(x^2-12x+12)`?

Answer 1

Two vertical asymptotes `x=10.899` or `x=1.101`

Explanation:

Using quadratic formulahe denominator `x^2-12x+12` will be zero at

`x=(12+-sqrt(12^2-4xx1xx12))/2=(12+-sqrt96)/2`or

`x=(12+-4sqrt6)/2=6+-2xx2.4495` i.e.

`x=10.899` or `x=1.101`

Hence we have two vertical asymptotes `x=10.899` or `x=1.101`.

As the degree of numerator is less than that of denominator, there is no horizontal or slanting asymptote.

graph{(x-2)/(x^2-12x+12) [-5, 20, -5, 5]}