This is referred to as a chestnut but it amuses me.
x = 1
Therefore: x² = x
x² - 1 = x -1
Factorising x² - 1 we get
(x - 1)(x + 1) = x - 1
Dividing both sides by (x - 1) we get:
x + 1 = 1
Substituting 1 for x we get:
2 = 1
Try this on a year 9 class last thing on a Friday afternoon.
I dare you.