$\begin{array}{l}\phantom{\phantom{;}x^{2}-4x\phantom{;}-3;}{\phantom{;}x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-4x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{3}-10x^{2}+14x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-4x\phantom{;}-3;}\underline{-x^{3}+4x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}+4x^{2}+3x\phantom{;};}-6x^{2}+17x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-4x\phantom{;}-3-;x^n;}\underline{\phantom{;}6x^{2}-24x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}6x^{2}-24x\phantom{;}-18\phantom{;}\phantom{;}-;x^n;}-7x\phantom{;}-27\phantom{;}\phantom{;}\\\end{array}$

$x-6+\frac{-7x-27}{x^2-4x-3}$