could any one give me a hint for this one? please not the whole solution Let f be a non constant rational function and ${z}_{1},\dots ,{z}_{n}$ be its poles in $\overline{\mathbb{C}}$. we have to show that f can be written as $f={f}_{1}+\dots ,{f}_{p}$ where each ${f}_{j}$ is a rational function.