2 = 1

Solution

'Cancelling' the common factors from line (4) to (5) means dividing by the factor (X-Y). Since X=Y, this is a division by 0, the results of which are undefined.

(1)     X = Y                        Given
(2)     X2 = XY                      Multiply both sides by X
(3)     X2 - Y2 = XY - Y2             Subtract Y2 from both sides
(4)     (X + Y)(X - Y) = Y(X - Y)    Factor both sides
(5)     (X + Y) = Y                  Cancel out common factors
(6)     Y + Y = Y                    Substitute in from line (1)
(7)     2Y = Y                       Collect the Y's
(8)     2 = 1                        Divide both sides by Y

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