Yeah, scouring a tank removing what is mostly beneficial bacteria and cleaning the filter any more than what you should usually be doing because you have a wounded fish is bonkers just as using salt in a freshwater tank is not a good idea especially with gold fish as they are more sensitive to it than many fish.
If someone is giving advice that could cause harm I'm calling them on it.
Most of the slime on the inside glass of aquariums is biofilm that contains harmful bacteria, viruses, protozoa and fungus. Removing this biofilm reduces the chance of infection.
Cleaning the filter regularly helps remove rotting fish waste that is a home to harmful protozoa and bacteria. All the aquarium water passes through the filter several times an hour. If you have a dirty filter full of rotting fish waste, the fish are living in dirty water with lots of harmful disease organisms.
Gravel cleaning the tank and doing big water changes helps remove rotting fish waste and more of the harmful bacteria, fungus and protozoa.
These 3 steps make a huge difference to the number of disease organisms in the aquarium and significantly increase the chance of the fish surviving, and significantly reduces the chance of secondary infections entering the damaged tissue.
These are the 3 main steps we did to any aquarium in the shop that had sick fish in. And if fish started looking off colour, they were the first things we did to the tank, and it usually brought about an instant improvement in the fish.
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As for salt, it is safe for all freshwater fish including goldfish that can tolerate huge amounts and are even found in slightly brackish water in some parts of Australia.
Salt can kill some bacteria, fungus and protozoan parasites and is a lot safer than most of the chemical based medications on the market, many of which contain things like Formaldehyde, which is a preservative used for embalming bodies. Many contain Malachite Green to treat external protozoa. Malachite Green (aka Victoria green) is a carcinogen.
Personally, I would rather swim in slightly salty water for a few weeks and even drink salt water, than swim in water containing Formaldehyde and Malachite Green. And there's no way I would want to drink water containing either of those chemicals.
When I have a choice of using salt, which has relatively minor side effects on freshwater fish, or a hazardous, poisonous chemical based medication that will kill everything in the tank if it's slightly overdosed, I choose salt because it's safer.
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This is my opinion based on over 40 years of fish keeping and working in wholesale and retail fish stores, dealing with hundreds of tanks in each facility. Looking after tens of thousands of fish at any one time. And treating all sorts of fish diseases ranging from minor Saprolegnia fungal infections, to white spot, to Fish TB. I have tried chemical based medications and antibiotics on numerous occasions. I have mixed different treatments in an attempt to cure fish. I tried no medications. I tried heat and cool and salt. And salt, combined with cleaning the tank, works quite well for a lot of minor issues.
In this case the fish has a damaged tail caused by being attacked by another fish. Cleaning the glass, gravel, filter, and changing the water, will help reduce the chance of secondary infections from bacteria, fungus and external protozoan parasites, and this will give the fish the best chance of healing. The salt will also reduce the number of disease organisms in the water and reduces the chance of secondary infections.
These are simple steps anyone can take if they have a sick or injured fish and can usually bring about a good response. At the very least it buys the fish and fish keeper time to work out what is going on, and work on a backup plan. If chemicals/ medications are required, the medication will work better in a clean tank with little to no gunk. The medication will be able to work on the fish and not get wasted killing microscopic organisms on the glass, in the substrate, filter media, or the water.
It is up to the individual what they do to their fish. I am only here to help. My advice is free and I try to offer safer alternatives to helping fish get through health issues. If other people want to use chemicals instead of clean water and salt, that is up to them. But I am not trying to harm your fish and not trying to sell you anything. The information I provide is based on decades of fish keeping and experimenting on fish to try and keep them alive. I have seen just about every sort of fish disease there is. I don't want people to go through what I went through learning about fish. I want people to be able to easily keep fish and have their fish remain healthy for as long as possible.
And I do practice what I preach. I use salt in my own tanks when required and I used it with all sorts of fishes ranging from tetras, to angelfish, guppies to goldfish and even Corydoras catfish. I have never killed a fish with salt but have killed fish with chemicals.