Find the horizontal asymptote
The Attempt at a Solution
There are two ways I did this problem. One way seems to be a coincidence and the other the "proper way"
1. I used long division, and got 2+(9x-3)/(x^2-2x)
2 seems to be the horizontal asymptote of the function
2.If we remove the highest degree terms from the function you end up with (2+(5/x) -(3/x))/(-2/x) with 2 being the horizontal asymptote.
Which is the proper method and why is it that everything I've ran into so far displays this.