Simplify

[Annihilist]

What do you guys get for this?

I fucked it up majorly by trying to expand first.

[z4lis]

Homework or not?

Either way, I would try to get rid of the fractions as much as possible. For instance,

\frac{\frac{1}{x^2} + \frac{1}{y^2}}{\frac{1}{x^2}-\frac{1}{y^2}} = \frac{x^2 + y^2}{y^2 - x^2}

by multiplying top and bottom by x²y². Try that for the other terms and see if it helps.

[zmic]

I get -1

Note that the factor in the bottom right :

(\frac{x^2}{y^2}+\frac{y^2}{x^2}-2)

is equal to

(\frac{x}{y}-\frac{y}{x})^2

[Qaanol]

Unless x=0 or y=0 or x=y or x=-y or x²=-y², in which case the whole thing is undefined.

[Nyktos]

I got 2xy/(x² + y²), but I'm very much willing to believe I made a mistake somwhere.

[Annihilist]

Not homework. I found it on a school related forum, but it's unrelated to school.

[Proginoskes]

I get -1

So does Maple.

[Catmando]

I got this comparatively bizarre answer

\frac{1}{16(x^2+y^2)^2}

which I suppose could be a bit more elegantly expressed as

\frac{1}{(4x^2+4y^2)^2}

I'm currently working back through my work to see where I went wrong (I've already found one mistake, as the above is actually my second result so far), because I doubt that's the right answer.

[TheWaterBear]

I got this comparatively bizarre answer

\frac{1}{16(x^2+y^2)^2}

which I suppose could be a bit more elegantly expressed as

\frac{1}{(4x^2+4y^2)^2}

I'm currently working back through my work to see where I went wrong (I've already found one mistake, as the above is actually my second result so far), because I doubt that's the right answer.

Plugged into Wolfram, reduces to -1, provided the conditions others have previously mentioned are met.

http://www.wolframalpha.com/input/?i=%28%281%2Fx^2%2B1%2Fy^2%29%2F%281%2Fx^2-1%2Fy^2%29-%281%2Fx^2-1%2Fy^2%29%2F%281%2Fx^2%2B1%2Fy^2%29%29%2F%288%2F%28%28%28x%2By%29%2F%28x-y%29%2B%28x-y%29%2F%28x%2By%29%29*%28%28x^2%2Fy^2%2By^2%2Fx^2-2%29%29%29

[Catmando]

Okay, I see what I did wrong. I assumed it was (stuff/8)/stuff instead of stuff/(8/stuff). I redid the problem earlier today and got a much better answer, and after checking (stuff/8)/stuff it seems I did it right in that respect. WA says that's

-\frac{x^4y^4}{4(x^4-y^4)^2}

Thanks!

[Qaanol]

In one line, here is the condition which, if met, renders the original form undefined:

x⁵y = y⁵x

[gfauxpas]

In one line, here is the condition which, if met, renders the original form undefined:

x⁵y = y⁵x

Hey neat, how'd you combine all the restraints into one equation like that?

[Tirian]

In one line, here is the condition which, if met, renders the original form undefined:

x⁵y = y⁵x

Hey neat, how'd you combine all the restraints into one equation like that?

Unless x=0 or y=0 or x=y or x=-y or x²=-y², in which case the whole thing is undefined.

x=0 or y=0 or x=y or x=-y or x²=-y²
<=>
x=0 or y=0 or x-y=0 or x+y=0 or x²+y²=0
<=>
(x)(y)(x-y)(x+y)(x²+y²) = 0
<=>
x⁵y-y⁵x=0
<=>
x⁵y = y⁵x

[benoitowns]

I remember getting that same, exact, obnoxious equation on a math quiz once...

[Afif_D]

I remember getting that same, exact, obnoxious equation on a math quiz once...

And so were you able to solve it?

[benoitowns]

I remember getting that same, exact, obnoxious equation on a math quiz once...

And so were you able to solve it?

If I remember correctly, I made some simple mistakes that led me to the wrong answer.