The tap extractors have saved my a$$ many times. Working in a machine shop in my previous life, the "tink" of broken taps was common.
After using thread cutting oil used primarily for the pipe threading machine for years, we were introduced to Tap Magic cutting fluid. From personal experience, this stuff greatly reduced the number broken taps. I'm not sure where it can be found as we got ours from an industrial supplier. I'm sure a google search would turn up a source.
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Bill