I can do [a procedure]
mechanically but don't know
why it works. Explain where
it comes from, what it's
really doing, and one case
where it would mislead.

Why the Method Works, Not Just How

The reasoning under the procedure, plus where it breaks.

Prompt

I can do [a mathematical procedure] mechanically but I don't understand why it works. Explain where the method comes from, what it's really doing, and show one case where blindly applying it would give a wrong answer.