# Awesome Roots Of Unity

Algebra Level 5

$\large{\dfrac{1}{m-\alpha}+\dfrac{1}{m-\alpha^2}+\cdots+\dfrac{1}{m-\alpha^n}}$

Let $$P(z)=z^{n+1}-1$$ have roots $$1, \alpha, \alpha^2, \ldots, \alpha^n$$ where $$\alpha$$ is a $$(n+1)^\text{th}$$ root of unity and $$m$$ isn't a $$(n+1)^\text{th}$$ root of unity.

Find the value of the expression above.

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