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

$2a^{4}+2a^{3}-5a^{2}+3a-2+\frac{5}{2a+1}$