$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-10;}{\phantom{;}x^{3}+9x^{2}+91x\phantom{;}+909\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-10\overline{\smash{)}\phantom{;}x^{4}-x^{3}+x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-10;}\underline{-x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+10x^{3};}\phantom{;}9x^{3}+x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-10-;x^n;}\underline{-9x^{3}+90x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-9x^{3}+90x^{2}-;x^n;}\phantom{;}91x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-10-;x^n-;x^n;}\underline{-91x^{2}+910x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-91x^{2}+910x\phantom{;}-;x^n-;x^n;}\phantom{;}909x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-10-;x^n-;x^n-;x^n;}\underline{-909x\phantom{;}+9090\phantom{;}\phantom{;}}\\\phantom{;;;-909x\phantom{;}+9090\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}9089\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+9x^{2}+91x+909+\frac{9089}{x-10}$