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If you have a discontinuity and you can cancel factors in the numerator and the denominator, then it is removable. If you can't cancel those factors to get rid of the discontinuity it is nonremovable. Here is an example that shows both kinds.

f(x) = (x - 2)(x + 3) /[(x - 2) (x - 4)

There is a discontinuity at x=2 but we can cancel out(x-2) from the top and bottom.

That makes it removable. However, at x=4 there also a discontinuity and there is no way to remove that one.

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Q: What is unremovable discontinuity?
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