Question 1152278
You take that x-3 and divide it by the 4 you factored out earlier.  That gives you the right asymptote.  It is messier, but you can also divide 4x+8 into the function and deal with fractions. You will get a slant asymptote of y=(1/4)x-(3/4), which is the same thing.

{{{graph(300,300,-10,10,-10,10,(x^2-x-2)/(4x+8),(x-3)/4)}}}