Check your signs. I'm pretty sure the fraction should be subtracted instead of added.
Once you have "x^2 - 4x + 11 - 17/(x+2) = ax^2 + bx + c + d/(x+2)", do what they call "equating coefficients": the variables and fraction parts are all the same (after the division) so the coefficients have to be the same. So x^2 = 1x^2 = ax^2, so it has to be a = 1. Etc. Get all the coefficients. Then add them up.
It occurred to me that each side looked very similar, and so I did try to do as you suggest, but with the sign mistake I'd made in front of the fraction on the left, it didn't work of course. At least when I waste so much time trying to figure something out because of a mistake that could easily have been caught, it ingrains the idea in my head to go back and _double-check_.
Thanks again for the help!
BTW, do you know if graphing calculators are able to equate coefficients? I assume that they are. I tried entering the problem in my calculator (ti-89), to see if I could get -9, and it returned an error message of some sort. I believe that I chose Solve(). Then after the equation, put ",a+b+c+d"
I am still familiarizing myself with the calculator, so I'm sure that I just entered things incorrectly. For instance, I used the "Alpha" button to get a,b,c,d into the equation, and I'm not sure if that is allowed.
Anyway, thanks again.