Adding that "u" is not needed. In your equation you have:

From this we want to factor out the highest power of X that occurs in the denominator, and we are left with:

From here, we know that 1/x approaches 0 as x approaches infinity in either direction. And thus we are left with:

Which is just 2/5.

This part here, is where you start to confuse yourself. Why are there negatives added on to the 2 and the 5?im -2(-x)+3

x->-∞ -5(-x)+7

This is fine (well not really since it's got those negatives but the process is the same), but then you make a mistake here:- lim u(-2 + (3/u))

u->∞ u(-5 + (7/u))

The u's cancel out, but you have made one u negative and the other positive, so they cancel but leave over a -1. Just little errors that are making big problems.-u(-2)

u(-5)