What is wrong with the following algebraic manipulation? A = B AA = AB AA - BB = AB -BB (A+B) (A-B) = B (A-B) A + B = B
Step 2 can be omitted. Simply go from step 1 to step 3 by multiplying both sides by A. Step 5 will draw the attention of the quadratic equation police.
I understand. Step five usually has that effect. You are correct about step 2. I will edit it. Thanks.
a-b =0 hence division by it is not allowed since the result becomes indeterminate. eg: how many times 0's are = 1? follow this link. http://forum.allaboutcircuits.com/showthread.php?t=6034
surely (A+B)(A-B) = (A+B)*0 = 0 and B(A-B) = B*0= 0 therefore (A+B)(A-B)=B(A-B) is true.. (?) .. Where does division come into this? As for A+B=B I do not understand this at all.. Surely this would be 2A or 2B ? Maths is my weakness, so I presume I am missing something basic..
then this, what happened here? the (A-B) got canceled . what math operation allows this cancellation? the answer is division. but for division there is a condition that divisor must not be zero (in maths at 'later' levels it becomes customary to mention that divisor is not zero b4 dividing) meaning cancellation is not allowed. edit: else: 5*0= 378975892749848929472*0 dividing both sides by zero (note this ain't allowed) 5= 378975892749848929472. or for that matter any number will become equal to any other number. eg;1= infinity,etc. (getting my point?)
(A + B) (A - B) = 2B (A - B), but since in this case A = B, and therefore A - B = 0, we can say that (A + B) (A - B) = B (A - B). However, since A - B = 0, both sides will be 0, independently of the remaining multipliers. Therefore you have an equation that simply states that 0 = 0. You can't also assume that A + B = B by dividing both sides by A - B, which is 0. It is an absurd.
Hmmm.. ok, I think I see it now.. It looks 'silly' when one is given A = B in the first place.. but if one was only given (A+B) (A-B) = B (A-B), without knowing that A=B, and tried to reduce this by division, one would end up with an absurd.. (?).. But if A != B, then (A+B) (A-B) = B (A-B) could not be true.. (?)
Of course, you are correct. The algebra class, I was in, was given this little algebraic manipulation in my first year of high school [1962]. No one was able to figure it out. It was a creative way to remind the class of the rule: Never divide by zero.
Further to my thread which recca linked to, the problem lies in the incorrect final two lines: For: (A+B) (A-B) = B (A-B) Where: A = B Then: (A+B) (A-B) = B (A-B) equates to (A+B)*0 = B*0 Which gives: 0 = 0 and not the final line of A + B = B (See http://forum.allaboutcircuits.com/showpost.php?p=34509&postcount=3) It does confuse you at first. Dave