$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}x^{2}-3x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{3}-6x^{2}+8x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+3x^{2};}-3x^{2}+8x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{\phantom{;}3x^{2}-9x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}-9x\phantom{;}-;x^n;}-x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}x\phantom{;}-3\phantom{;}\phantom{;}-;x^n-;x^n;}-9\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x-1+\frac{-9}{x-3}$