Answer:

For all x in [0, 2] except x ’= 1, we know that f[x] = (x^2 - 1)/(x - 1). We can algebraically simplify f[x] by canceling common factors:

Cancel[f[x]]

This says that for all not equal to 1, f[x] = x + 1. This says that for all x in [0, 2] that are different from 1, f[x] and x+1 have the same value. Since we can't see a single, isolated point (like x = 1), the graph of f[x] should look just like the graph of x+1.