Final answer to the problem
$x^{2}-2+\frac{x}{x^2+2}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^4+x-4$ by $x^2+2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+2;}{\phantom{;}x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}+x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2;}\underline{-x^{4}\phantom{-;x^n}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{2};}-2x^{2}+x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n;}\underline{\phantom{;}2x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}2x^{2}+4\phantom{;}\phantom{;}-;x^n;}\phantom{;}x\phantom{;}\phantom{-;x^n}\\\end{array}$
2
Resulting polynomial
$x^{2}-2+\frac{x}{x^2+2}$
Final answer to the problem
$x^{2}-2+\frac{x}{x^2+2}$