# Sum of a faithfully flat module and a flat module

For a ring $R$, a left $R$-module $F$ is flat if the functor $- \otimes_R F$ brings an exact sequence of right $R$-modules to an exact sequence of right $R$-modules.

It is faithfully flat if the functor $- \otimes_R F$ brings a sequence of right $R$-modules to an exact sequence of right $R$-modules if and only if the original sequence is exact.

It is a "standard fact" that the sum of a faithfully flat module and a flat module is faithfully flat. Can someone please explain why this is true.