Can I put one of my Goldfish in with my Tropical fish?

Most likely, they are not being bullied. Goldfish rarely bother other fish. The real problem lies with the size of the tank. Goldfish need a relatively large tank. 30 gallons or more is best. If they are not put in a aquarium of that size, they get a bit worn around the edges, especially if there's a lot of rough structure in your tank. The structure can shred fancy Goldfish's tails very easily. Removing the sharp structure should cure the problem. Instead of the pointy structure, add more plants or other smooth structure.