Final Answer
$x^{2}+10+\frac{91}{x^2-9}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^4+x^2+1$ by $x^2-9$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-9;}{\phantom{;}x^{2}\phantom{-;x^n}+10\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-9\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-9;}\underline{-x^{4}\phantom{-;x^n}+9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+9x^{2};}\phantom{;}10x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-9-;x^n;}\underline{-10x^{2}\phantom{-;x^n}+90\phantom{;}\phantom{;}}\\\phantom{;-10x^{2}+90\phantom{;}\phantom{;}-;x^n;}\phantom{;}91\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{2}+10+\frac{91}{x^2-9}$
Final Answer
$x^{2}+10+\frac{91}{x^2-9}$