Im having a bit of difficulty recalling how to go about this. I remeber that to search for the horizontal asymptotes I would solve to find the limit of x > 0 from the left and right (sice there can only be 2 horizontal asymptotes. Heres the problem below:

solution:

I did everything to the point of x-2/(x(x-1)). Why does the x before x-1 mysteriously go away? I started to stray from the solution posted by canceling out the x in x-2 and the first x in the denominator, to get -2/-1 which = 2. What is the difference in procedure in searching for the limit of 0 from the left and the right? Thanks!