Let $\displaystyle S $ be a multiplicative set of $\displaystyle R $, and write $\displaystyle S^{-1}R $ for the ring of $\displaystyle S-$ fractions of $\displaystyle R $. Prove that the two functors $\displaystyle S^{-1}(\cdot) $ and $\displaystyle S^{-1}R \oplus_{R}(\cdot) $ from the category of $\displaystyle R $ modules to that of $\displaystyle S^{-1}R $ module are isomorphic.