$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}x^{3}+2x^{2}+6x\phantom{;}+22\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{4}-x^{3}\phantom{-;x^n}+4x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-x^{4}+3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+3x^{3};}\phantom{;}2x^{3}\phantom{-;x^n}+4x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-2x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}+6x^{2}-;x^n;}\phantom{;}6x^{2}+4x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-6x^{2}+18x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{2}+18x\phantom{;}-;x^n-;x^n;}\phantom{;}22x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-22x\phantom{;}+66\phantom{;}\phantom{;}}\\\phantom{;;;-22x\phantom{;}+66\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}74\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+2x^{2}+6x+22+\frac{74}{x-3}$