How do I show that if $U$ is open in $X$ and $A$ is closed in $X$, then $U-A$ is open in $X$, and $A-U$ is closed in $X$?

So far I have that $X-A$ and $U$ are open, hence $U \cap (X-A)$ is open. I need to show that $U \cap (X-A)=U-A$, but I don't know how to do so. Thanks for your help.