My two dogs fight when I put a plate of food down for one of them. Can I let them fight it out so they stop this behavior?

I have got 2 female dogs which fight not all the time, only when they get jealous such as if we put a plate down for one of them and the other one comes over they start growling and then they start to have an aggressive fight. I have read how to separate them but I would like to know would they kill each other if we left them, or is they any training we could teach them to stop fighting full stop.

Thanks
Letty