help with limits?

Question

Determine and classify the points of discontinuity in each of the following:

f (x)= x-1/(x+3)(x-2)

f (x)= x3-27/x2-9

Answer 1

For the first one, you know when x=-3 or x=2, the denominator goes to zero. Therefore, you have a discontinuity in the function. You also know, none of them cancel out. The fact that they don't cancel out makes it non-removable discontinuity.

For the second one, if you factor both sides, you'll see there are common factors between denominator and numerator. Because they are common, they cancels out. That makes it removable discontinuity. Of course, the x value in denominator that makes the factor zero denotes the discontinuity in the function, regardless of if they cancel out or not.