Got a question about a simple proof.
Prove: If \[\frac{ x }{ x-1 } \le 2\] then x < 1 or x >= to 2.
I approached this by multiplying both sides by (x-1), and factoring out x, which simplified to 2 <= x.
I feel like this satisfies the hypothesis, but I feel like something is missing. I guess I just don't see how this is PROOF. Is it just that simple and I am missing the fundamental connection, or am I just way off base?

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Thanks a ton, I had a feeling something was missing!

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