OpenSAT

A removable discontinuity occurs at a point where the function is undefined due to a zero in the denominator, but the limit of the function exists at that point. In this case, the function is undefined when *x* = 2 because it results in a zero in the denominator. However, the function can be simplified by factoring the numerator: $f(x) = \frac{x^2 - 4}{x-2} = \frac{(x+2)(x-2)}{x-2} = x+2$ for all *x* not equal to 2. Therefore, the limit of *f* as *x* approaches 2 exists and is equal to 4. Since the limit exists, the function has a removable discontinuity at *x* = 2.