What rational functions will have a hole at x2?

Answer 1

A rational function is undefined - you might say that it "has a hole" - at any point where the denominator is zero. Assuming you mean "... hole at x = 2", any rational function which has the factor (x-2) in its denominator will have a hole at x = 2.

Answer 2

Any function, which in its simplified form, has a factor of (x - 2) in the denominator is undefined for x = 2. I am not sure if this constitutes a "hole".