z-transform and roc

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I am a bit confused. I have the function \begin{equation} F(z)= \frac{2z}{z^2 -1} \end{equation} So I get two poles, in 1 and -1. But I am a bit confused, which is my region of convergence? Should it be between 1 and -1 ? Also, normally I find the z-transform always with $z^{-1}$. Can I directly work with my function, or should I transform it so that I have $z^{-1}$ instead of $z$ ? Thanks!