The Impossible !

Here is a proof that many of you may have come across. It is nothing more than a mathematical parlour trick and is quite obviously a fallacy. See if you can spot where it all falls apart and save the math world !

let a = b
a² = ab..........................................................Multiply both sides by a
a² + a² - 2ab = ab + a² - 2ab.....................Add (a² - 2ab) to both sides
2(a² - ab) = a² - ab......................................Factor the left, and collect like terms on the right
2 = 1...............................................................Divide both sides by (a² - ab)

Amazing isn't it??!! Yet all the operations are correct there is nothing wrong with the algebra or arithmetic at all but there is one thing they overlooked, either deliberately or not, but I think it is deliberate no mathematician can be that stupid. Found it yet? Lemme give you a hint, look closely at the part where you divide both sides by (a² - ab). I hope you got it. If not then leave a comment and I will let you in on the secret but with the hint I feel you should be able to find where the fallacy lies.