I actually had a betta and a fantail goldfish live very happily together in a 5 gallon tank, until I moved them and my heater stopped working midwinter.
The goldfish was only about an inch in total when I bought it, the betta full grown; but they swam together slept side by side all the time and never went after each other. once the goldfish got to be about 2 inches long I got a 10gallon tank and they loved it, I tried a few guppies but that didnt last, I tried a pleco and that didnt work, so I was going to leave them til the gold fish got too big and give to someone witha pond except I grew up in an old house on a farm and one night in the winter the power went out and I lost the betta, it was only about a week or so and I lost the goldfish.
just showing that incompatible fish can live together just like a dog raising ritten or whatever.