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

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