I have to prove the above question. So, if $P$ is projective then there exist a $Q$ such that $P\bigoplus Q=F'$ where $F'$ is free. I was thinking that may be we should take $F(Q)-$ free module generated by $Q$ and show that $P\bigoplus F(Q)=F'$. But how to do it, I don't know. Can anybody help?
Thank you