Let $R$ be an integral domain with fraction field $K$. For a fractional ideal $I$ (i.e. $I$ is an $R$-submodule of $K$ such that $\exists 0\ne r\in R $ with $rI \subseteq R$) of $R$, define $(R:I)=\{x\in K : xI \subseteq R\}$.
Is it true that $(R:I\cap J)=(R:I)+(R:J)$ for $I,J$ fractional ideals?
I can easily see that $(R:I)+(R:J) \subseteq (R:I\cap J)$, however I am having difficulty proving $(R:I\cap J) \subseteq (R:I)+(R:J)$.