$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}4x^{2}-10x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}4x^{3}-6x^{2}+2x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-4x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}-4x^{2};}-10x^{2}+2x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}10x^{2}+10x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}10x^{2}+10x\phantom{;}-;x^n;}\phantom{;}12x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-12x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;;-12x\phantom{;}-12\phantom{;}\phantom{;}-;x^n-;x^n;}-21\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}-10x+12+\frac{-21}{x+1}$