$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}3x^{2}-17x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}3x^{3}-14x^{2}+7x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-3x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-3x^{2};}-17x^{2}+7x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}17x^{2}+17x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}17x^{2}+17x\phantom{;}-;x^n;}\phantom{;}24x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-24x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{;;-24x\phantom{;}-24\phantom{;}\phantom{;}-;x^n-;x^n;}-20\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-17x+24+\frac{-20}{x+1}$