Complex Oblique Asymptote problem

Hello,

I'm currently taking Grade 12 advance functions math and our teacher assigned an interesting question for us to work through over the weekend.

I have to graph the following equation which includes an Oblique Asymptote:

X^3 + 4x^2 + x - 6 / x^2 + 3x + 2

The first thing I did was factor the denominator and received (X+1) (X+2).

I believe I now have to do long division to determine the roots for the equation in the numerator. I was thinking about using:

X^3 + 4x^2 + x - 6 / X+1 but when I do I come up with the answer x^2 + 3x - 2.

Can someone offer some assistance on how to tackle this problem? I've used my graphing calculator to see how the graph looks and there is also a 'hole' in it as well.

Any assistance would be appreciate because I really have no idea where to go from here.

Thanks