(X^-2 +X^-1)÷(X+X^-3)

$$\\(X^{-2} +X^{-1})\div(X+X^{-3})\\\\
=(\frac{1}{X^{2}} +\frac{1}{X^{1}})\div(X+\frac{1}{X^{3}})\\\\
=\frac{1+X}{X^{2}} \div\frac{X^4+1}{X^{3}}\\\\
=\frac{1+X}{X^{2}} \times \frac{X^{3}}{X^4+1}\\\\
=\frac{1+X}{1} \times \frac{X}{X^4+1}\\\\
= \frac{X(X+1)}{X^4+1}\\\\$$

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