You can
put this solution on YOUR website!
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?
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The step in red is the mistake.
You're dividing by zero there. That's because -x+b-a = 0.
How do we know that -x+b-a = 0?
From the original assumption x = b - a which clearly
shows that -x+b-a = 0
Take the original assumption:
x = b - a
Multiply both sides by -1
-x = -b + a
Add b - a to both sides:
-x+b-a = 0
Therefore -x+b-a equals 0 by the original
assumption and you can't divide by 0.
Edwin
