If your fish have frayed fins they probably have Goldfish Fin Rot. This disease is caused by a bacterial infection that leads to irritation and inflammation of the fins leading to their erosion.
Single cell parasites, like goldfish ich, are often involved as well. They injure the fishes skin and allow entry of the bacteria.
Most tanks with fish that have fin rot have poor water quality conditions which decreased the immune system of it's fish. It is of utmost importance to improve the water quality conditions for your fish to improve.
The bacteria and fungal infections can usually be easily treated with medication available at local or on-line pet stores. With proper treatment the fins will usually heal back completely.