$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{3}-x^{2}+7x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}+6x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-x^{3};}-x^{3}+6x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+x^{2}-;x^n;}\phantom{;}7x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-7x^{2}-7x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-7x^{2}-7x\phantom{;}-;x^n-;x^n;}-7x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}7x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}7x\phantom{;}+7\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-3\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-x^{2}+7x-7+\frac{-3}{x+1}$