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

[aerf]

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

 

[HomogenousCow]

Do you mean x/y+y/x=(x^2+y^2)/xy
Because your original equality is false

 

[Mentallic]

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?

 

[aerf]

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.

 

[Mentallic]

6 = 2*3 isn't it? And with any fraction of the form \frac{x}{y} it is also equivalent to \frac{ax}{ay} 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?