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

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