Goldfish with bettas are a no no. First because goldfish are cold water fish, whereas bettas are tropicals who need much warmer temperatures. Also because bettas generally don't tolerate other larger fish very well, especially ones with long fins. I'm guessing that the betta would either attack the goldfish, or be completely terrified (depending on his "personality")!
the goldfish produce too much muck in the water for the bettas. I found this out when I had had my black moor in a tank for only a couple of days i then got an emergency betta, goldfish out betta in, poor betta nearly snuffed it.
Do you have trouble with sb with your fish my poor moore spends half his life upside down?