Final answer to the problem
$x^{4}+4x^{2}+16+\frac{64}{x^2-4}$
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1
Divide $x^6$ by $x^2-4$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-4;}{\phantom{;}x^{4}\phantom{-;x^n}+4x^{2}\phantom{-;x^n}+16\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-4\overline{\smash{)}\phantom{;}x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}-4;}\underline{-x^{6}\phantom{-;x^n}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{6}+4x^{4};}\phantom{;}4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x^{2}-4-;x^n;}\underline{-4x^{4}\phantom{-;x^n}+16x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{4}+16x^{2}-;x^n;}\phantom{;}16x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x^{2}-4-;x^n-;x^n;}\underline{-16x^{2}\phantom{-;x^n}+64\phantom{;}\phantom{;}}\\\phantom{;;-16x^{2}+64\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}64\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{4}+4x^{2}+16+\frac{64}{x^2-4}$
Final answer to the problem
$x^{4}+4x^{2}+16+\frac{64}{x^2-4}$
