Is there a short form for this equation?

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Discussion Overview

The discussion revolves around the attempt to find a compact form for the equation S = A + L/(B+C) + L/(B-C), with participants exploring whether it is valid to express it as S = A + L/(B±C). The conversation evolves to a more complex version of the equation involving additional terms, specifically S = A + L/(D+(B+C)²) + L/(D+(B-C)²).

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the validity of expressing S = A + L/(B+C) + L/(B-C) as S = A + L/(B±C), suggesting it leads to incorrect interpretations.
  • Another participant proposes an alternative form, S = A + 2 L B/(B² - C²), but this is also challenged.
  • There is a clarification regarding the introduction of a term D in the equation, with participants discussing its necessity based on the complexity of the denominators.
  • One participant insists that the equation is already in its simplest form and expresses a desire to condense it for publication purposes.

Areas of Agreement / Disagreement

Participants express differing opinions on the validity of the proposed compact forms and whether the introduction of D is necessary, indicating that multiple competing views remain without consensus.

Contextual Notes

The discussion includes unresolved questions about the simplification of the equation and the implications of introducing additional terms, particularly the term D, which complicates the expression.

TheIsingGuy
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I am trying to write down a compact form of[STRIKE] S = A+L/(B+C)+L/(B-C), does it make sense in general to write down S = A+L/(B[itex]\pm[/itex]C)?[/STRIKE]

Update:

I have simplified it too much in the minimal working example, the denominators is actually more complicated, let me elaborate:

[itex]S=A+\frac{L}{D+(B+C)^{2}}+\frac{L}{D+(B-C)^{2}}[/itex]

Any ideas?
 
Last edited:
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No, it does not make sense to write it that way.

What was wrong with S = A + 2 L B/(B^2 - C^2)?
 
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TheIsingGuy said:
I am trying to write down a compact form of S = A+L/(B+C)+L/(B-C), does it make sense in general to write down S = A+L/(B[itex]\pm[/itex]C)?
If you write like that, it means the answer is:
##S=A+\frac{L}{B+C} or S=A+\frac{L}{B-C}##
Which is not correct.
 
I have simplified it too much in the minimal working example, the denominators is actually more complicated, let me elaborate:

[itex]S=A+\frac{L}{D+(B+C)^{2}}+\frac{L}{D+(B-C)^{2}}[/itex]

Any ideas?
 
TheIsingGuy said:
I have simplified it too much in the minimal working example, the denominators is actually more complicated, let me elaborate:

[itex]S=A+\frac{L}{D+(B+C)^{2}}+\frac{L}{D+(B-C)^{2}}[/itex]

Any ideas?
From where did this ##D## come from?
 
D is supposed to be there, I had ignored the square in the first post, in which case D is not necessary. Now it is. Any ideas how to simplify it now?
 
TheIsingGuy said:
D is supposed to be there, I had ignored the square in the first post, in which case D is not necessary. Now it is. Any ideas how to simplify it now?
Show us your attempt
 
adjacent said:
Show us your attempt

This is not homework, I believe it is the simplest form, some people might even recognise the equation (it's a famous one), I just wanted it to fit in 1 line on a double column publication
 

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