Is 2 = 1?

Algebra Level 1

What is wrong with the following "proof"?

Let \(a = b=1\), then \(a=b.\)

  • Step 1: \(a^2 = ab \)
  • Step 2: \(a^2 - b^2 = ab - b^2 \)
  • Step 3: \((a+b)(a-b) = b(a-b) \)
  • Step 4: \(a+b= \dfrac{b(a-b)}{a-b} \)
  • Step 5: \(a+b = b\)

Conclusion: By substituting, \( a = b = 1 \implies 1+1 = 1 \implies 2 = 1.\)

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