$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}{\phantom{;}x^{3}+3x^{2}+10x\phantom{;}+27\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}+2x^{3}\phantom{-;x^n}+3x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}\underline{-x^{5}+3x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+3x^{4}-x^{3};}\phantom{;}3x^{4}+x^{3}\phantom{-;x^n}+3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n;}\underline{-3x^{4}+9x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{4}+9x^{3}-3x^{2}-;x^n;}\phantom{;}10x^{3}-3x^{2}+3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n;}\underline{-10x^{3}+30x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-10x^{3}+30x^{2}-10x\phantom{;}-;x^n-;x^n;}\phantom{;}27x^{2}-7x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-27x^{2}+81x\phantom{;}-27\phantom{;}\phantom{;}}\\\phantom{;;;-27x^{2}+81x\phantom{;}-27\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}74x\phantom{;}-29\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+3x^{2}+10x+27+\frac{74x-29}{x^2-3x+1}$