Fraction Decomposition: A/a+B/b?

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Discussion Overview

The discussion revolves around the possibility of expressing the fraction 1/(a + b) in terms of A/a + B/b. Participants explore whether such a transformation is feasible and the implications of any resulting expressions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if 1/(a + b) can be manipulated into a form like A/a + B/b.
  • Another participant suggests that while it may be possible, the constants A and B could depend on a and b or even be zero, potentially limiting the usefulness of such a transformation.
  • A further response indicates skepticism about the general feasibility of the original question, suggesting that any derived expressions may not be practical, referencing a specific manipulation that appears to be ineffective.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of transforming 1/(a + b) into A/a + B/b, with some indicating it may be possible under certain conditions while others argue it is generally not feasible.

Contextual Notes

Participants note that the usefulness of any derived expressions may be limited by the dependencies of A and B on a and b, as well as the potential for these constants to be zero.

priced02
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Just wondering - is there anything you can do with 1/(a + b) to get something like A/a + B/b?
 
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character string manipulations
 
yes, but your B's and A's may be in terms of a and b or even 0. Making it kind of useless...
 
lalbatros said:
character string manipulations

lol... by the way, I don't think the original question is possible in general. of course, as JonF mentioned... you can have:

[tex]a\cdot\frac{\frac{1}{a+b}}{2a}+b\cdot\frac{\frac{1}{a+b}}{2b}[/tex]

which is utterly useless.
 

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