$\begin{array}{l}\phantom{\phantom{;}2x^{2}+3;}{\phantom{;}8x^{4}\phantom{-;x^n}-12x^{2}\phantom{-;x^n}+18\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}+3\overline{\smash{)}\phantom{;}16x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+243\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}+3;}\underline{-16x^{6}\phantom{-;x^n}-24x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-16x^{6}-24x^{4};}-24x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+243\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}+3-;x^n;}\underline{\phantom{;}24x^{4}\phantom{-;x^n}+36x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}24x^{4}+36x^{2}-;x^n;}\phantom{;}36x^{2}\phantom{-;x^n}+243\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}+3-;x^n-;x^n;}\underline{-36x^{2}\phantom{-;x^n}-54\phantom{;}\phantom{;}}\\\phantom{;;-36x^{2}-54\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}189\phantom{;}\phantom{;}\\\end{array}$

$8x^{4}-12x^{2}+18+\frac{189}{2x^2+3}$