[rfurmani]

You have two functions both of which grow to infinity, one of which is much better understood than the other. It turns out that if you subtract the two functions, they balance out perfectly so you end up with something converging to 4 instead of going to infinity.

[powertower]

When you subtract any two functions that are exponential, the answer is 4?

[Slickarango]

Not quite. Take two exponentially growing functions, say e^x and e^2x over the interval [0,infinity). as x-> infinity both grow without bound. So does the difference of e^(2x)-e^x because the former is just so much larger than the second. They both approach infinity, but at different rates! If the difference between two functions (in the limit) converges, that means that the two functions diverge at the same rate (i.e. both with the end behavior of e^(ax) for some constant a) This is all a little hand wavy though but I hope that clears things up.