I need help in proving the following.
Given $Q$ a polynomial evaluated over the complex numbers such that $\alpha_1, ..., \alpha_n$ are roots of $Q$ and $P$ a polynomial such that $\deg P<n$ prove that $$ \frac{P(z)}{Q(z)}=\sum_{k=1}^{n}\frac{P(\alpha_k)}{Q'(z)(z-\alpha_k)} $$ At first I tried kind of 'brute forcing' from one side and then the other and I think I got farther when beginning with the right side but still I didn't manage to get the identity. Any help is appreciated.