$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}-6x\phantom{;}+14\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}-5x^{2}+8x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}-6x^{2}+8x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}6x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{2}+6x\phantom{;}-;x^n;}\phantom{;}14x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-14x\phantom{;}-14\phantom{;}\phantom{;}}\\\phantom{;;-14x\phantom{;}-14\phantom{;}\phantom{;}-;x^n-;x^n;}-18\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-6x+14+\frac{-18}{x+1}$