# What is the discontinuity of the function #f(x) = (x^2-9)/(x^2-6x+9)# ?

##### 1 Answer

f a rational expression (basically a fraction with a polynomial in the numerator and another polynomial in the denominator) has a discontinuity, it will be where the denominator equals zero.

So for

The key to the next step is remembering how to factor.

So there is some type of discontinuity at

Now there are two types of discontinuity possible here.

If

If

Let's see:

This is an interesting case. We removed the discontinuity, but instead of a hole in the graph, we have a vertical asymptote at the exact same point.

Hope this helps.