Home > Calculus > Classifying Topics of Discontinuity (removable vs. non-removable)

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

Answer 1

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

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)#

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Answer 2

Adam Adkins

The discontinuity of the function (x-2) / (x-2)(x+2) occurs at x = -2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.