I am supposed to find the hole in this expression: x^2-4/x^2-4x+4. It gets reduced to (x+2)(x-2)/(x-2)^2. My book says the hole is when x equals two, but I would think it would be -2, since x-2 and x-2 cancel each other out. Why is this? Thanks ~Shealyn

Note: This answer assumes the expression is parenthesized as (x^2 - 4) / (x^2 - 4x + 4).

Either you made a mistake, I did, or the book did. The graph of that expression doesn't have a hole. It does, however, have a vertical asymptote at x=2. Are you sure you're supposed to find a hole in the graph, not an asymptote, or just a point where the value of the expression is undefined?