$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+1;}{\phantom{;}2x^{2}-x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+1\overline{\smash{)}\phantom{;}4x^{3}\phantom{-;x^n}+7x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+1;}\underline{-4x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}-2x^{2};}-2x^{2}+7x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n;}\underline{\phantom{;}2x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{2}+x\phantom{;}-;x^n;}\phantom{;}8x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n;}\underline{-8x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;;-8x\phantom{;}-4\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}5\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-x+4+\frac{5}{2x+1}$