State Runge's theorem about uniform approximation of holomorphic functions by polynomials.

Let $\mathbb{R}_{+} \subset \mathbb{C}$ be the subset of non-negative real numbers and let

$$\Delta=\{z \in \mathbb{C}:|z|<1\} .$$

Prove that there is a sequence of complex polynomials which converges to the function $1 / z$ uniformly on each compact subset of $\Delta \backslash \mathbb{R}_{+}$.