How to find a Slant Asymptote - does this method work?

Say it's y = (x^2 -3x +2) / (x - 4)


If I divide every term in this by x (and let x tend to infinity) I will get


(x - 3) / 1 which is y = x - 3


Is that the slant asymptote?


If not, why not?How to find a Slant Asymptote - does this method work?
you can divide syntheticaly


1 -3 2


4} 4 4


1 1 6


so the asymptote would be x+1 and you just forget about the remainder of 6