$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}-1;}{\phantom{;}x^{2}+3x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}+5x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-1;}\underline{-x^{4}+3x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+3x^{3}+x^{2};}\phantom{;}3x^{3}+x^{2}+5x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-1-;x^n;}\underline{-3x^{3}+9x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{3}+9x^{2}+3x\phantom{;}-;x^n;}\phantom{;}10x^{2}+8x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-1-;x^n-;x^n;}\underline{-10x^{2}+30x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{;;-10x^{2}+30x\phantom{;}+10\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}38x\phantom{;}+10\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+3x+10+\frac{38x+10}{x^2-3x-1}$