If A=B
Multiply both sides by A, you get A²=AB.
Subtract B² from both sides, you get A²-B²=AB-B².
Factor both sides make it (A+B)(A-B)=B(A-B).
Divide both sides by (A-B), you get A+B=B.
Because A=B, therefore B+B=B,
If 2B=B, then 2=1.
Similar puzzle can also be seen at http://www.omardo.com/en/:
Math Puzzle
(2=1).
Answer
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The problem is when you try to divide both sides by (A-B).
Because A=B, therefore (A-B)=0.
You can't divide any equation by zero.