I'm not sure how advanced your definition of continuity is. In the most elementary terms, a function is continuous at a point b if 1) the limit of the function at b exists and 2) it equals .
You can see that has a removable discontinuity at . So, the limit exists at 0, but the actual value of the function is undefined (because that pesky x in the denominator becomes zero, and dividing by zero is undefined). So, if we simply define , we have defined the function so that the limit at 0 exists, and the function takes on the value of the limits. So, m=3.