Where did C go?!?

Take the equation below, trace the steps, and tell me what happened to variable C.





A = B + C (multiply both sides by (A - B))





A(A - B) = (A - B)(B + C) (multiply this out)





A^2 - AB = AB + AC - B^2 - BC (now subtract AC from both sides)





A^2 - AB - AC = AB - B^2 - BC (now simply each side by factoring)





A(A - B - C) = B(A - B - C) (now divide both sides by (A - B - C)





A = B (what happened to C?! My original equation stated that A = B + C, not that A = B. Where did C go?)

Where did C go?!?
If A = B + C, then A - B = C, and (A - B - C) = C - C = 0, and you have ended up dividing by 0 which is not allowed.
Reply:Hi,


in your original equation:


A=B+C or A-B=C


At the end of the statements,


In short, you are saying


A=B


=%26gt; A-B=0 or =C=0





you need to think that...
Reply:You are dividing by zero





(A - B - C) = 0





Since





A = B + C





Hence,





A - B - C = 0





When you divide by zero, you can equate anything.


{Hence the answer is indeterministic and not useful}








A (A - B - C) = B (A - B - C)





A (0) = B (0)





e.g. 123 (0) = 4 (0) is also true.





You can then claim,





123 = 4


{obviously, this is false}





The value of C when A = B, is C = 0.





But this is immaterial since A = B is erroneous in the first place when you divide by zero by cancelling out the term (A - B - C).
Reply:The answer is simple A-B-C=0 .


you mustn't divide by 0.
Reply:It's magic...





HAHAHAHA... just kidding...





You can't just divide the (A-B-C) because according to the first equation, A= B+C.





Rearrange this equation, A-B = C, once more... A-B-C = 0





And you can't divide by a zero...
Reply:You can't divide by 0 in mathematics.





A = B + C,


so A - B - C = 0.





Not allowed. Bad bad bad. Don't do it.
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