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

$4a-2+\frac{3}{2a+1}$