Assume A + B = C, and assume A = 3 and B = 2.
Multiply both sides of the equation A + B = C by (A + B).
We obtain A² + 2AB + B² = C(A + B)
Rearranging the terms we have
A² + AB – AC = – AB – B² + BC
Factoring out (A + B – C), we have
A(A + B – C) = – B(A + B – C)
Dividing both sides by (A + B – C), that is, dividing by zero, we get A = – B, or A + B = 0, which is evidently absurd.
I found this delouse paradox from http://www.paradoxes.co.uk
You can’t divide by (a + b – c) because the result is undefined.
Look at it this way. if you rearrange the INITIAL equation, by subtracting c from both sides you get “a + b – c = 0″, right? What happens on your calculator if you divide any number by zero (try it with 5 / 0)? The result is undefined. But we know that a + b – c = 0 so you cannot divide by it!!! Therefore your paradox isn’t really a paradox because it doesn’t violate any rule of mathematics.