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How do I understand this?


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How do I show, prove, see or be convinced that


I am concerned with what is going on in the minus sign there. I do remember that the following holds:


Or that

[math](-1)(-1)=+1[/math] or just 1.

I also remember that [math]\frac{(-1)}{(-1)}=1[/math] or just 1 or that [math]\frac{(-)}{(-)}=+[/math]. What can I make of these identities in being convinced or cleared of what is obscured to me.

Edited by Chikis
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If you are used to re-formulating terms the identity is obvious. So it is a bit hard for me to guess what could be the blocker to your understanding. Perhaps this very simple statement helps:


The minus sign in front of your fraction "belongs" to the nominator, i.e.

[math] - \frac{bp}{cp - a} = \frac{-bp}{cp - a} [/math]


If that did not help yet (I recommend trying to go on from this first step by yourself before reading the 2nd hint):



Multiplying a term by 1 does not change it. Neither does multiplying with [math]\frac{-1}{-1}[/math], since that equals 1.



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How do I show, prove, see or be convinced that

If we have equation in form:



We can multiply both sides by b and receive:



Then multiply both sides by d and receive:




In your case it's:



so after rearranging it's:





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  • 5 weeks later...

I am fond of interpreting the situation like "distribution of the minus(literally -1)", rather than multiplying the nominator and denominator by -1.

If you "move" the - to the denominator space, where (cp-a) becomes (a-cp) that do the trick.

Note: You can multiply right side denominator by -1 which is the same. However, I suggest getting rid of minuses, than creating new minus signs on the leading left side numbers..

Edited by TransientResponse
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