Proof of (a/b).(c/d)-1 = (a.d)/(b.c) | Better Method for Homework

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Homework Help Overview

The discussion revolves around proving the equality \((a/b)/(c/d) = (a.d)/(b.c)\) through different methods. Participants are exploring various algebraic manipulations and proofs related to fractions and their operations.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants present different algebraic approaches to proving the equality, questioning which method might be more elegant or preferable. There is a comparison of two proofs, with some expressing preferences for one over the other.

Discussion Status

The discussion includes multiple perspectives on the proofs presented, with participants sharing their thoughts on elegance and correctness. Some express satisfaction with their approaches while others acknowledge corrections and preferences.

Contextual Notes

There appears to be a playful tone in the discussion, with participants using informal language and emojis. The context suggests a collaborative environment where participants are encouraged to share and critique each other's methods.

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Homework Statement


proof (a/b)/(c/d) = (a/b).(c/d)-1 = (a.b-1).(c.d-1)-1 = (a.b-1)(d.c-1)=(a.d).(b-1.c-1) = (a.d).(b.c)-1 = (a.d)/(b.c)



Homework Equations





The Attempt at a Solution



the other way to proof (a/b).(c/d)-1 = [(a.b-1)/(c.d-1)].(d/d-1) = (a.d.b-1)/(c.d.d-1) =(a.d.b-1)/c = (a.d)/(b.c)

which one is better proof ?
 
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i mean in more elegant way ..oh yea thanks before ..
 
dianzz said:

Homework Statement


proof (a/b)/(c/d) = (a/b).(c/d)-1 = (a.b-1).(c.d-1)-1 = (a.b-1)(d.c-1)=(a.d).(b-1.c-1) = (a.d).(b.c)-1 = (a.d)/(b.c)



Homework Equations





The Attempt at a Solution



the other way to proof (a/b).(c/d)-1 = [(a.b-1)/(c.d-1)].(d/d-1) = (a.d.b-1)/(c.d.d-1) =(a.d.b-1)/c = (a.d)/(b.c)

which one is better proof ?

you mean d/d:wink:


all works well, though I prefer the first
 
drizzle said:
you mean d/d:wink:


all works well, though I prefer the first

yea you right ..thanx for correcting:wink:

mm..you prefer the first ,but i dontnow I am suite with the last :biggrin:..
 

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