What is wrong with the proof?

Algebra Level 3
  1. Let \(x\) be a solution of \(x^{2} + x + 1 = 0\)
  2. Since \(x\) is not 0, we can divide both sides by \(x\):
    • \(x + 1 + \frac{1}{x} = 0\)
  3. Substitute \(x + 1 = -x^{2}\)
    • \(\frac{1}{x} = x^{2}\)
  4. \(x = 1\)
    • \(x = x^{3}\)
  5. \(3 = 0\)
    • \(1^{2} + 1 + 1 = 0\)
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