2 = 1?!?

Little Johnny went to his teacher one day after a lesson in algebra and claimed that he had managed to prove that 2 actually equals to 1. This is the proof that he provided:

x = 2

Multiply both sides of the equation by (x-1) to get:

x(x-1) = 2(x-1)

x²-x = 2x-2

x²-2x = x-2

x(x-2) = x-2

Divide both sides of the equation by (x-2) to get:

x = 1

Therefore 2 = 1

Does this really mean that 2 = 1? If not, at which step in the working did he go wrong?

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