f(x)=x²-5x+7/(x-2)

It asks me to give the vertical, horizontal and slant asymptotes if there are any.

This is what I have so far:

vertical asymptote: x cannot equal 2

I am now trying to find the slant asymptote by synthetic (long division) because x²-5x+7 does not factor out.

I am really stuck so may someone show me how to do this problem? I still need to find the slant and horizontal asymptotes.