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a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a - b)(a + b) = b(a - b)
(a - b)(a + b) = b(a - b)
(a + b) = b

but\ a = b
therefore:

a + a = a
2a = a

hence

2 = 1

However, this results in dividing by 0, because a - b = a - a = 0


EDIT:

Your mistake comes in step 5, when you divided by (x-y) on both sides. 
Since x = y, x-y = 0, so you are dividing by zero, which is undefined 
(illegal!). 

Source: http://mathforum.org/library/drmath/view/55792.html

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