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

1 Answer
VNVDVI
Apr 15, 2018

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)#

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