Adding Fractions: Solve x/y + y/x = x^2 + y^2/xy

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Discussion Overview

The discussion revolves around the equation x/y + y/x = x^2 + y^2/xy, with participants exploring its validity and the process of adding fractions. The scope includes mathematical reasoning and clarification of algebraic expressions.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the equation and seeks clarification on its truth.
  • Another participant points out that the original equality may be incorrect and suggests a different interpretation of the equation.
  • A participant reiterates the original equation and emphasizes the importance of proper notation, specifically the use of brackets.
  • Discussion includes a reference to adding fractions, using the example of 1/2 + 2/3 to illustrate the process of finding a common denominator.
  • One participant explains the equivalence of fractions and the necessity of equal denominators for addition.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the original equation, with some suggesting it may be incorrect while others seek to clarify the notation and process involved.

Contextual Notes

There is ambiguity regarding the interpretation of the equation due to the lack of brackets, which affects the understanding of the mathematical expression. Additionally, the discussion does not resolve whether the original equation holds true.

aerf
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Just stumbled upon something and I've never been taught it before and cannot see why its true... Hoping someone can help

x/y + y/x = x^2 + y^2/xy

Thanks
 
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Do you mean x/y+y/x=(x^2+y^2)/xy
Because your original equality is false
 
aerf said:
Just stumbled upon something and I've never been taught it before and cannot see why its true... Hoping someone can help

x/y + y/x = x^2 + y^2/xy

Thanks

Clearly you implied (x2+y2)/xy as opposed to x2+(y2/xy) and to see why this is true, do you know how to add fractions such as 1/2+2/3?
 
Mentallic said:
Clearly you implied (x2+y2)/xy as opposed to x2+(y2/xy) and to see why this is true, do you know how to add fractions such as 1/2+2/3?

Yeah I just forgot my brackets... It came when simplifying this trigonometric equation and just changed from the one form to the other and I got so confused so I looked at what happened and came to that equation, yes but I'd only make the denominators 6 and then add the numerators.
 
6 = 2*3 isn't it? And with any fraction of the form [tex]\frac{x}{y}[/tex] it is also equivalent to [tex]\frac{ax}{ay}[/tex] for any a (assuming the values aren't equal to 0), and the only way you can add fractions is if their denominators are equal.

So, what did you do to 1/2+2/3 to solve it, and how can you apply that to your original question?
 

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