$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}4x^{3}-9x^{2}-6x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}4x^{4}-x^{3}-24x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-4x^{4}-8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}-8x^{3};}-9x^{3}-24x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}9x^{3}+18x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}9x^{3}+18x^{2}-;x^n;}-6x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}6x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6x^{2}+12x\phantom{;}-;x^n-;x^n;}\phantom{;}12x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-12x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{;;;-12x\phantom{;}-24\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-34\phantom{;}\phantom{;}\\\end{array}$

$4x^{3}-9x^{2}-6x+12+\frac{-34}{x+2}$