SOLUTION: The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw? Let a and b be any two different numbers. Define x as the differenc

Question 150442: The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw?
Let a and b be any two different numbers. Define x as the difference between them:
x = b - a
Multiply both sides of the equation by (b-a):
x(b � a) = (b � a)(b � a)
bx � ax = b^2 � 2ab + a^2
Add �bx+ab-a^2 to both sides and simplify:
bx � ax � bx + ab � a^2 = b^2 � 2ab + a^2 � bx + ab � a^2
bx � bx � ax + ab � a^2 = �bx + b^2 � 2ab + ab + a^2 � a^2
�ax + ab � a^2 = �bx + b^2 � ab
Both sides of this equation have a common factor:
a(�x + b � a) = b(�x + b � a)
Divide both sides by (-x+b-a):
a(�x + b � a)/-x + b-a = b(�x + b � a)/ -x + b - a
a = b

What was my mistake?

Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
You said "Divide both sides by (-x+b-a)"
But what is x?
x = b-a
So what is (-x + b -a)?
(-b + a + b - a) = 0
You can make 'anything' happen if you allow division by zero. Which is why division by zero is undefined.

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