$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{3}-5x^{2}+12x\phantom{;}-17\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{4}-4x^{3}+7x^{2}-5x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-x^{3};}-5x^{3}+7x^{2}-5x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}5x^{3}+5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}+5x^{2}-;x^n;}\phantom{;}12x^{2}-5x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-12x^{2}-12x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-12x^{2}-12x\phantom{;}-;x^n-;x^n;}-17x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}17x\phantom{;}+17\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}17x\phantom{;}+17\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}8\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-5x^{2}+12x-17+\frac{8}{x+1}$