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, \( a = b = 1 \) , \(1+1 = 1 \ , \ 2 = 1 \) .

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