$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}3x^{2}+2x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}3x^{3}-4x^{2}-12x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-3x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}+6x^{2};}\phantom{;}2x^{2}-12x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;-2x^{2}+4x\phantom{;}-;x^n;}-8x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}8x\phantom{;}-16\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}8x\phantom{;}-16\phantom{;}\phantom{;}-;x^n-;x^n;}-6\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}+2x-8+\frac{-6}{x-2}$