Is 2 = 1?

Algebra Level 1

What is wrong with the following "proof"?

Let a=b=1a = b=1, then a+b=b.a+b=b.

  • Step 1: a2=aba^2 = ab
  • Step 2: a2b2=abb2a^2 - b^2 = ab - b^2
  • Step 3: (a+b)(ab)=b(ab)(a+b)(a-b) = b(a-b)
  • Step 4: a+b=b(ab)aba+b= \dfrac{b(a-b)}{a-b}
  • Step 5: a+b=ba+b = b

Conclusion: By substituting in a=b=1, a = b = 1, we have 1+1=1    2=1.1+1 = 1 \implies 2 = 1.

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