$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}{\phantom{;}3x^{2}+10x\phantom{;}+32\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}+1\overline{\smash{)}\phantom{;}3x^{4}+x^{3}+5x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}\underline{-3x^{4}+9x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+9x^{3}-3x^{2};}\phantom{;}10x^{3}+2x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n;}\underline{-10x^{3}+30x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{;-10x^{3}+30x^{2}-10x\phantom{;}-;x^n;}\phantom{;}32x^{2}-9x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n;}\underline{-32x^{2}+96x\phantom{;}-32\phantom{;}\phantom{;}}\\\phantom{;;-32x^{2}+96x\phantom{;}-32\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}87x\phantom{;}-37\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}+10x+32+\frac{87x-37}{x^2-3x+1}$