How can I prove that $\text{Tor}_1(R/I,R/J) = (I \cap J)/IJ$, where $R$ is a ring and $I, J$ ideals. 

Moreover, if we suppose $R=I+J$, how do I prove that $\text{Tor}_1(R/I,R/J)=0$?


Ps: No, this is not a homework question.