$\begin{array}{l}\phantom{\phantom{;}2x^{2}-4x\phantom{;}+3;}{\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}-4x\phantom{;}+3\overline{\smash{)}\phantom{;}2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}2x^{2}-4x\phantom{;}+3;}\underline{-2x^{3}+4x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}+4x^{2}-3x\phantom{;};}\phantom{;}4x^{2}-3x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}2x^{2}-4x\phantom{;}+3-;x^n;}\underline{-4x^{2}+8x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;-4x^{2}+8x\phantom{;}-6\phantom{;}\phantom{;}-;x^n;}\phantom{;}5x\phantom{;}-6\phantom{;}\phantom{;}\\\end{array}$

$x+2+\frac{5x-6}{2x^2-4x+3}$