(X^-2 +X^-1)÷(X+X^-3)

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