Too good to pass up...

I know this is old, but let's prove that 2 = 1.

• Let a and b be equal non-zero quantities
  
  a = b


• Multiply through by a
  
  a² = ab


• Subtract b²
  
  a² − b² = ab − b²


• Factor both sides
  
  (a − b)(a + b) = b(a − b)


• Divide out (a − 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

Who can spot the fallacy?

Works Cited

"Invalid proof". Wikipedia. 26 Feb 2007. <http://en.wikipedia.org/wiki/False_proof>