Dividing by zero

[StealthySkeptic]

Here's a little trick I like to play on people, many of you have probably seen it before.

Given

a = b

Multiply both sides by a

a^2 = ab

Subtract b^2 from both sides

a^2 - b^2 = ab - b^2

Factorize both sides, LHS is difference of two squares.

(a+b)(a-b) = b(a-b)

Cancel out the (a-b) on both sides

(a+b) = b

But since a=b

b+b = b

2b = b

Cancel out the b on both sides

2 = 1