# Oblique Asymptotes: What happens to the Remainder?

Let's say I'm trying to find the oblique asymptote of the function:

f(x)=
-3x2 + 2
x-1

Forgive my poor formatting.

So because the denominator isn't linear, we do polynomial long division of the function and ultimately get -3x - 3 as our quotient, with a remainder of -1. For the sake of the oblique asymptote, we disregard the remainder. But why? I haven't found a website that explains it; they all simply say to ignore the remainder. It bothers me that we just forget about it, regardless of what it is.
Can you explain to me why we disregard the remainder, and where it "goes?"

$$\frac{-3x^2+ 2}{x- 1}= -3x- 3- \frac{1}{x- 1}$$