# How do I understand this?

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

$-\frac{bp}{cp-a}=\frac{bp}{a-cp}$

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

$(-)(-)=+$

Or that

$(-1)(-1)=+1$ or just 1.

I also remember that $\frac{(-1)}{(-1)}=1$ or just 1 or that $\frac{(-)}{(-)}=+$. 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:

$- \frac{bp}{cp - a} = \frac{-bp}{cp - a}$

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 $\frac{-1}{-1}$, since that equals 1.

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Do I take it that

$\frac{-bp}{cp}=\frac{bp}{-cp}$?

Edited by Chikis
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Yes, that is correct.

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

If we have equation in form:

$\frac{a}{b}=\frac{c}{d}$

We can multiply both sides by b and receive:

$a=\frac{b*c}{d}$

Then multiply both sides by d and receive:

$a*d=b*c$

$-\frac{bp}{cp-a}=\frac{bp}{a-cp}$

so after rearranging it's:

$-(bp*(a-cp))=bp*(cp-a)$

$-(bp*a-bp*cp)=bp*cp-bp*a$

$-bp*a+bp*cp=bp*cp-bp*a$

$bp*cp-bp*a=bp*cp-bp*a$

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Alright, thank you for the asistance.

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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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