$\begin{array}{l}\phantom{\phantom{;}2x^{2}+1;}{\frac{1}{2}x^{7}\phantom{-;x^n}+\frac{-\frac{1}{2}}{2}x^{5}\phantom{-;x^n}+\frac{\frac{1}{4}}{2}x^{3}\phantom{-;x^n}+\frac{-\frac{1}{8}}{2}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}2x^{2}+1\overline{\smash{)}\phantom{;}x^{9}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}2x^{2}+1;}\underline{-x^{9}\phantom{-;x^n}-\frac{1}{2}x^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{9}-\frac{1}{2}x^{7};}-\frac{1}{2}x^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}2x^{2}+1-;x^n;}\underline{\phantom{;}0.5x^{7}\phantom{-;x^n}+\frac{1}{4}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}0.5x^{7}+\frac{1}{4}x^{5}-;x^n;}\frac{1}{4}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}2x^{2}+1-;x^n-;x^n;}\underline{-0.25x^{5}\phantom{-;x^n}-\frac{1}{8}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-0.25x^{5}-\frac{1}{8}x^{3}-;x^n-;x^n;}-\frac{1}{8}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}2x^{2}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}0.125x^{3}\phantom{-;x^n}+\frac{1}{16}x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}0.125x^{3}+\frac{1}{16}x\phantom{;}-;x^n-;x^n-;x^n;}\frac{1}{16}x\phantom{;}\phantom{-;x^n}\\\end{array}$

$\frac{1}{2}x^{7}-\frac{1}{4}x^{5}+\frac{1}{8}x^{3}-\frac{1}{16}x+\frac{\frac{1}{16}x}{2x^2+1}$