2x^3-2x^2-6x+7÷x^3-3x+2

What is your question? I assume:

3x^3 - 2x^2 - 9x + 9

or, using partial fractions,

2 - (5/9)/(x+2) - (13/9)/(x-1) + (1/3)/(x-1)^2