$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+7;}{\phantom{;}x^{2}-7x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+7\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-46x\phantom{;}+22\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+7;}\underline{-x^{3}-7x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-7x^{2};}-7x^{2}-46x\phantom{;}+22\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+7-;x^n;}\underline{\phantom{;}7x^{2}+49x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{2}+49x\phantom{;}-;x^n;}\phantom{;}3x\phantom{;}+22\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+7-;x^n-;x^n;}\underline{-3x\phantom{;}-21\phantom{;}\phantom{;}}\\\phantom{;;-3x\phantom{;}-21\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$

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