Let $K$ be a field and let $Z=\frac{X^3}{X+1} \in K(X)$.
Show that $K(X)$ is an algebraic extension of degree 3 of $K(Z)$.
I am trying to figure out first why $Z\in K(X)$ as I don't know that the field K(X) contains the inverse of $(X+1)$. I only know that it contains X so it contains $X^{-1}$
Thank you for your help.