I just posted this in the other thread:

Long division is one of those "pay your dues" kind of topics. You should do some of it, but don't grind it to death. It is laborious, and it's not surprising it takes a while (but one should just get stuck into it and get it over and done with). It is important to understand how and why it works, so later you'll have no problem with (e.g.)

x^3/(x-2)=x^2+2x+4+(8/(x-2))