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

$x^{2}+2x-1+\frac{9x+6}{2x^2+x-2}$