I am doing an exercise from "an introduction to homological algebra by Charles A.Weibel" and I am not able to get it, but if the following comes true then I think I can solve the exercise, but I don't know whether the following is true or not.
Let $M$ and $N$ are free $R$-modules. Let $L$ be an $R$-module such that $M \cong L \oplus N$. Does it implies that $L$ is a free $R$-module.
Please help me.