BrainBashers – Puzzle ZIHG – ??

A Proof That 2 = 1:
let X = Y:

           X = Y

multiply by X on both sides:

         X.X = X.Y

subtract Y.Y from both sides:

   X.X - Y.Y = X.Y - Y.Y

factorise:

  (X + Y)(X - Y) = Y(X - Y)

divide by (X - Y) on both sides:

       (X + Y) = Y

replace X with Y:

         Y + Y = Y

factorise:

          2Y = Y

divide by Y on both sides:

           2 = 1

Where lies the flaw in the logic?

Puzzle & Answer – www.brainbashers.com/zihg