This is a classical mathematical fallacies. At hindsight, everything looks perfectly fine.

So did you manage to spot the error? It is at line 5, where we divide both sides of the equation by $a-b$. Now this is mathematical alright, but in this case, it is not! notice that $a-b=0$ on the account that we started with $a=b$. And we need to be reminded that we cannot divide anything by zero.

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