$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}{\phantom{;}3x^{3}+3x^{2}+6x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}+1\overline{\smash{)}\phantom{;}3x^{5}-6x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}\underline{-3x^{5}+9x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{5}+9x^{4}-3x^{3};}\phantom{;}3x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n;}\underline{-3x^{4}+9x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{4}+9x^{3}-3x^{2}-;x^n;}\phantom{;}6x^{3}-3x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n;}\underline{-6x^{3}+18x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{3}+18x^{2}-6x\phantom{;}-;x^n-;x^n;}\phantom{;}15x^{2}-6x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-15x^{2}+45x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;;;-15x^{2}+45x\phantom{;}-15\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}39x\phantom{;}-17\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+3x^{2}+6x+15+\frac{39x-17}{x^2-3x+1}$