The reason that when nature divides by 0 that black holes are created is as follows

Eventually when you get to the speed of light (the c in the aforementioned equation) you end up subtracting C – C (I mixed them up before it was S – C that is the part of the denominator), this creates the entire denominator as a 0. Mass and Time are variables and the closer you get to C with your speed the more mass you get and the less time you have. When S = your speed, and you speed becomes the speed of light, making C – C in the denominator then the denominator becomes 0. When this happens you mass becomes infinite and you time becomes 0, which makes a black hole. This is amazing because mass and time are supposed to be constants.

That is what my teacher told me yesterday when I asked. Hope that clears it up for you Fenix as to why when nature divides by 0 it makes black holes :D