Just pointing out something...I know it's a really old thread !Someone pointed out earlier that for something like y= \frac{2x^2+5x+11}{x+1} you can just divide by "x" and get that the asymptote is: y= \frac{2x+ 5+ \frac{11}{x}}{1+ \frac{1}{x}}
However, that is not the case I...