Simplify

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Simplify

Postby Annihilist » Sat Mar 31, 2012 2:04 pm UTC

Image

What do you guys get for this?

I fucked it up majorly by trying to expand first.
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Re: Simplify

Postby z4lis » Sat Mar 31, 2012 2:50 pm UTC

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.
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Re: Simplify

Postby zmic » Sat Mar 31, 2012 3:08 pm UTC

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
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Re: Simplify

Postby Qaanol » Sat Mar 31, 2012 4:25 pm UTC

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

Postby Nyktos » Sun Apr 01, 2012 2:27 am UTC

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

Postby Annihilist » Sun Apr 01, 2012 5:45 am UTC

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

Postby Proginoskes » Sun Apr 01, 2012 7:43 am UTC

zmic wrote:I get -1


So does Maple.
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Re: Simplify

Postby Catmando » Wed Apr 04, 2012 12:57 am UTC

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.
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Re: Simplify

Postby TheWaterBear » Wed Apr 04, 2012 3:01 pm UTC

Catmando wrote: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
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Re: Simplify

Postby Catmando » Wed Apr 04, 2012 3:56 pm UTC

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!
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Re: Simplify

Postby Qaanol » Wed Apr 04, 2012 7:04 pm UTC

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

x5y = y5x
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Re: Simplify

Postby gfauxpas » Wed Apr 04, 2012 8:59 pm UTC

Qaanol wrote: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?
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Re: Simplify

Postby Tirian » Thu Apr 05, 2012 4:14 am UTC

gfauxpas wrote:
Qaanol wrote: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?


Qaanol wrote: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
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Re: Simplify

Postby benoitowns » Sun Apr 22, 2012 4:44 pm UTC

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

Postby Afif_D » Wed May 02, 2012 4:18 am UTC

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


And so were you able to solve it?
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Re: Simplify

Postby benoitowns » Wed May 02, 2012 9:34 pm UTC

Afif_D wrote:
benoitowns wrote: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. :oops:
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