Hi, i was just wondering why f(2) is not defined in the expression below:

f(x) = (x^2 - x - 2) / (x - 2)

I factorised (x^2 - x - 2) to get (x - 2)(x + 1). I then cancelled the (x - 2) in the numerator and the denominator out. The final f(x) would be (x + 1).

However, my calculus textbook says that the function will still be discontinuous at x = 2.

May i ask the principle behind this? Hasn't (x - 2) already been removed from the denominator?