Answer
Check work for reasoning.
Work Step by Step
A removable discontinuity is a discontinuity that can be removed by simply "filling in" a point; it may be formed when the same factor cancels out from the numerator and the denominator.
A non-removable discontinuity is one that cannot be removed by simply "filling" in a point; it may be caused by the denominator of a fraction equaling $0$ for a certain value of $x.$
a)$\dfrac{(x+2)}{(x+4)}$ has a non-removable discontinuity at $x=-4$ since the denominator is $0$ at that point.
b)$\dfrac{(x+4)(x-4)}{(x-4)}$ has a removable discontinuity at $x=4$ since $(x-4)$ cancels out from both the numerator and the denominator.
c)$\dfrac{(x+2)(x-4)}{(x+4)(x-4)}$ has both a removable discontinuity at $x=4$ and a non-removable discontinuity at $x=-4.$
