I am having some confusion about holes in rational functions. As I'm aware, a hole is where both the numerator and denominator become zero due to some discontinuity. For example,
f(x) = (x+1)(x-1)/(x+1)
would have a hole at x = -1.
What is the point of distinguishing between a hole and Vertical Asymptote?
What is the logic behind the numerator needing to having a discontinuity at the same point as the denominator?