Q:

Let $I,J,K$ ideals of ring R. Prove that $I+JK \subseteq (I+J)(I+K)$

Let $I,J,K$ ideals of ring R. Prove that $I+JK \subseteq (I+J)(I+K)$
Comments: This is something I need to solve an exercise. Previously tasted the ring I'm working $IJ = I \cap J$ should the need arise. 
I'm trying to take $a \in I+JK$ and show including, but not out.
Thank for your help.

A:

Hint Can you show that $I+JK \subset (I+J) \cap (I+K)$?

