$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}{\phantom{;}x^{2}+3x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-x^{2}+2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}\underline{-x^{4}+3x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+3x^{3}-x^{2};}\phantom{;}3x^{3}-2x^{2}+2x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n;}\underline{-3x^{3}+9x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{3}+9x^{2}-3x\phantom{;}-;x^n;}\phantom{;}7x^{2}-x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n;}\underline{-7x^{2}+21x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{;;-7x^{2}+21x\phantom{;}-7\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}20x\phantom{;}-4\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+3x+7+\frac{20x-4}{x^2-3x+1}$