Looked under rat savvy vets, and saw one did amputations. Had one pts because of a broken leg and the vet said no to doing an amputation. So if someone has a 3-legged rat let me see it and tell if it's ok (I'll show it to my vet)
My mom's rat had a back leg amputated. It was a very successful surgery. The leg was removed because of a recurring fibrosarcoma.
How broken was your rat's leg? Some rats can live just fine with a broken leg, it heals, sometimes not in the right way but they can still adapt if there's not too much pain.
It would be great if you mention it to your vet, he'll keep learning.
Here's Sven, had the leg removed when he was 23 or 24 months old, lived to be 32 months.
Here he is using morats to groom himself, this was several months after the surgery:
A friend of mine has a rat that broke his leg a while back. She had him to the vet and they actually put the leg in a cast for I want to say three weeks, an amount of time the rat did not like. Anyway even after all of the setting and the cast it still did not really heal right and they opted to let it continue to heal on its own. Timothy (the rat) is doing great now, it never really healed right so he kind of walks funny on it but he is not in pain.
The vet at the time said that if it did not heal right they could consider amputation but it did not become necessary.
I'm going to pass this link on to Julia in hopes she can give you some more advice.