normalization of multiplicative subset of domain

I am stuck with this:

Let $R$ be a domain with normalization $R’ \subset K$. Show that for every multiplicative subset $S \subset R$, the normalization of $S^{-1}R$ equals $S^{-1}R’$.

How do you show this? I am not yet that into the definitions and theorems I could use to prove such a statement.

Hope someone feels like giving a hint or any help!! 🙂

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