How I separate 1/(2+1) in 2 fractions?

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Discussion Overview

The discussion revolves around the mathematical expression 1/(2+1) and various methods proposed by participants to separate it into two fractions. The scope includes mathematical reasoning and exploratory approaches to fraction decomposition.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant suggests that 1/(2+1) can be expressed as (1/3) + (0/3).
  • Another participant proposes that 1/(2 + 1) can be separated into 1/6 + 1/6.
  • A different participant mentions that 1/(2 + 1) could also be represented as 2/9 + 1/9, indicating multiple possible decompositions.
  • One participant provides a more complex derivation, showing that 1/(2+1) can be expressed as 1/2*(1/(1+1/2)), leading to a series expansion and further simplification resulting in 1/2 - 1/6.

Areas of Agreement / Disagreement

Participants present multiple competing views on how to separate the expression, with no consensus on a single method being preferred or established as correct.

Contextual Notes

Some methods presented rely on specific assumptions or manipulations that may not be universally applicable, and the discussion does not resolve the validity of each approach.

xeon123
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How I separate 1/(2+1) in 2 fractions?
 
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1/(2+1) = (1/3)+(0/3) :-p
 
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Or 1/(2 + 1) = 1/6 + 1/6
Or 1/(2 + 1) = 2/9 + 1/9
There are any number of ways to do it.
 
1/(2+1)=1/2*(1/(1+1/2))=1/2*(1-1/2+(1/2)^2-(1/2)^3+-+-)=1/2-1/4*(1-1/2+(1/2)^2-+-+)=1/2-1/4*2/3=1/2-1/6

For example. :smile:
 

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