What are the removable discontinuities of the following function? f of x is equal to the fraction with numerator x squared minus 36 and denominator x cubed minus 36 x

Factor the numerator and denominator: f(x) = (x − 6)(x + 6) / [x(x − 6)(x + 6)]. The factors x − 6 and x + 6 cancel, leaving 1/x, so x = 6 and x = −6 are removable discontinuities (holes). The factor x in the denominator does not cancel, so x = 0 is not removable. The correct choice is D, x = −6 and x = 6.

AI-written and checked against the verified answer.