Proof That 0 = 1?

Algebra Level 1

The following steps appear to give equivalent equations, which seem to prove that 1 = 0. Find the step that contains the error.

x = 1 GIVEN x^{2} = x MULTIPLY BY x x^{2} - x = 0 SUBTRACT x x(x-1) = 0 FACTOR x = 0 DIVIDE BY x-1 1 = 0 Given x = 1

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