$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+1;}{\phantom{;}x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+1\overline{\smash{)}\phantom{;}2x^{3}-x^{2}+3x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+1;}\underline{-2x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}-x^{2};}-2x^{2}+3x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n;}\underline{\phantom{;}2x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{2}+x\phantom{;}-;x^n;}\phantom{;}4x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n;}\underline{-4x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;-4x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}2\phantom{;}\phantom{;}\\\end{array}$

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