$S^{-1}R[(x_i)_{i\in I}]=(S^{-1}R)[(x_i)_{i\in I}]$

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Behold any commutative ring $R$. Is it true that $S^{-1}R[(x_i)_{i\in I}]=(S^{-1}R)[(x_i)_{i\in I}]$ for any multiplicative subset $R$ of $S$? I couldn't find this in full Bourbaki generality, not even in Bourbaki itself!