how to show that a function is an identity to broken rational functions

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Let be $ g \in \mathbb{Z} [X] $

$ g(X)= X^7 -7X^5+14 X^3-7X $

I don't know how to show that $$ g(X+ \frac{1}{X} )= X^7+ \frac{1}{X^7} $$

is an identity to broken rational functions.. Do you maybe have any Ideas?

Thank you for any help !