$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}x^{2}-2x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{3}-5x^{2}+7x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+3x^{2};}-2x^{2}+7x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{\phantom{;}2x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{2}-6x\phantom{;}-;x^n;}\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;;-x\phantom{;}+3\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}5\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-2x+1+\frac{5}{x-3}$