Is There a Simpler Way to Understand Mathematics?

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  • Thread starter Thread starter Sameh soliman
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Discussion Overview

The discussion revolves around the question of whether mathematical expressions can be simplified, specifically focusing on a particular expression involving variables x and y. Participants explore various methods of simplification and the implications of what "simplified" means in this context.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Some participants express uncertainty about their mathematical expertise, questioning if the expression can be simplified.
  • One participant provides a link to WolframAlpha, suggesting it offers a simplified form of the expression.
  • Another participant notes that the initial link provided does not work and offers a corrected version with proper parentheses.
  • A participant presents a simplified form of the expression as $$\frac{\sqrt{x^2 + y^2}}{y}+1$$ and suggests further simplification to a form involving a single variable expression.
  • Another participant proposes an additional simplification, expressing the result in terms of a new variable defined as ##z:=\dfrac{x}{y}##.
  • Some participants indicate that they are experiencing issues with the links shared in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on what constitutes a "simplified" form, and there are multiple approaches to simplification presented without agreement on a single method.

Contextual Notes

The discussion reflects varying interpretations of simplification and the challenges of communicating mathematical expressions clearly, particularly through links that may not function for all users.

Sameh soliman
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I am sorry but i am not a mathematician
Could this be simplified ?
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... or even one more step:
$$
\dfrac{\sqrt{x^2+y^2}}{y}+1=1+\sqrt{\left(\dfrac{x}{y}\right)^2+1}
$$
which gives a nice form with only one variable expression ##z:=\dfrac{x}{y}##.
 
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Links don't work for me either.
 

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