$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{-10x^{9}-30x^{8}-90x^{7}-270x^{6}-810x^{5}-2425x^{4}-7275x^{3}-21825x^{2}-65475x\phantom{;}-196425\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}-10x^{10}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+5x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{\phantom{;}10x^{10}-30x^{9}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}10x^{10}-30x^{9};}-30x^{9}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+5x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{\phantom{;}30x^{9}-90x^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}30x^{9}-90x^{8}-;x^n;}-90x^{8}\phantom{-;x^n}\phantom{-;x^n}+5x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}90x^{8}-270x^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}90x^{8}-270x^{7}-;x^n-;x^n;}-270x^{7}\phantom{-;x^n}+5x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{\phantom{;}270x^{7}-810x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}270x^{7}-810x^{6}-;x^n-;x^n-;x^n;}-810x^{6}+5x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}810x^{6}-2430x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;\phantom{;}810x^{6}-2430x^{5}-;x^n-;x^n-;x^n-;x^n;}-2425x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}2425x^{5}-7275x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;\phantom{;}2425x^{5}-7275x^{4}-;x^n-;x^n-;x^n-;x^n-;x^n;}-7275x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}7275x^{4}-21825x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;;\phantom{;}7275x^{4}-21825x^{3}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}-21825x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}21825x^{3}-65475x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;;;\phantom{;}21825x^{3}-65475x^{2}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}-65475x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}65475x^{2}-196425x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;;;;\phantom{;}65475x^{2}-196425x\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}-196425x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}196425x\phantom{;}-589275\phantom{;}\phantom{;}}\\\phantom{;;;;;;;;;\phantom{;}196425x\phantom{;}-589275\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}-589276\phantom{;}\phantom{;}\\\end{array}$

$-10x^{9}-30x^{8}-90x^{7}-270x^{6}-810x^{5}-2425x^{4}-7275x^{3}-21825x^{2}-65475x-196425+\frac{-589276}{x-3}$