$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{-3x^{2}-6x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}-3x^{3}\phantom{-;x^n}+8x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{\phantom{;}3x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}3x^{3}-6x^{2};}-6x^{2}+8x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{\phantom{;}6x^{2}-12x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{2}-12x\phantom{;}-;x^n;}-4x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}4x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}4x\phantom{;}-8\phantom{;}\phantom{;}-;x^n-;x^n;}-15\phantom{;}\phantom{;}\\\end{array}$

$-3x^{2}-6x-4+\frac{-15}{x-2}$