The more formal definition of this invalid proof (ie. the one that isn't a sloppy photoshopped graphic) has the values 'a' and 'b' defined as non-zero qualities. Besides the division by zero, the proof is sound.
Code:
Proof that 2 equals 1
Let a and b be equal non-zero quantities
a = b
Multiply through by a
aČ = ab
Subtract bČ
aČ minus bČ = ab minus bČ
Factor both sides
(a - b)(a + b) = b(a minus b)
Divide out (a minus b)
a + b = b
Observing that a = b
b + b = b
Combine like terms on the left
2b = b
Divide by the non-zero b
2 = 1
The fallacy is in line 5: the progression from line 4 to line 5 involves division by (a minus b), which is zero since a equals b. Since division by zero is undefined, the argument is invalid.