We say $U,V$ is a splitting of a Topological space $X$ if , $$ X = U \cup V $$
where $U,V$ are Open, disjoint , non empty subsets of $X$
In a book I'm reading it says that for any Compact Haussdorf topological space and given two distinct connected components, a splitting can be chosen such that they lie on different sides of the split.
My question is, how do we show this? I realize compact haussdorf implies Normal but I'm not able to make an explicit splitting using that.