$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+1;}{\phantom{;}2x^{2}+4x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+1\overline{\smash{)}\phantom{;}4x^{3}+10x^{2}-6x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+1;}\underline{-4x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}-2x^{2};}\phantom{;}8x^{2}-6x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n;}\underline{-8x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;-8x^{2}-4x\phantom{;}-;x^n;}-10x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}10x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}10x\phantom{;}+5\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}14\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+4x-5+\frac{14}{2x+1}$