Question

What are the discontinuities of `(x-2) / (x-2)(x+2)`?

Answer 1

Removable discontinuity (hole) at `(2, 4)`

Explanation:

We realize that `x-2` cancels out as follows:

`((x+2)cancel(x-2))/(cancel(x-2))=x+2`

This means that we have a removable discontinuity (hole) at `x-2=0,` or at `x=2`. To find the `y-`coordinate of the removable discontinuity, evaluate the simplified function at `x=2:`

`2+2=4`

So, there is a removable discontinuity at

`(2,4)`