Generalization of Sokhotski–Plemelj theorem

Question

Sokhotski–Plemelj theorem tells us, that

$ \frac{1}{x \pm i \cdot\epsilon} =\mp i \pi \delta(x) +V.p. \frac{1}{x}$

Is there an analogue of this theorem for some rational positive power $\alpha$ :

$ \frac{1}{(x \pm i \cdot\epsilon)^{\alpha}} =?$