I know a lot about fish, and that looks a lot like fungi -- one of my bettas had that. I just took my betta out of the water and pulled it off, it was at the tip of the tail but with the fungi being there it might be a problem since it has formed all the way around the fin, and if you were to pull it off you would be pulling off his fin as well, which would cause a big deal of pain. My best guess is that the goldie got his fin torn by another fish, it got infected and formed fungi. I don't know how to get rid of it in this case - but good luck.