Simplify
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 Posts: 76
 Joined: Mon Mar 05, 2012 12:29 pm UTC
Simplify
What do you guys get for this?
I fucked it up majorly by trying to expand first.
Re: Simplify
Homework or not?
Either way, I would try to get rid of the fractions as much as possible. For instance,
[math]\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}[/math] by multiplying top and bottom by x^{2}y^{2}. Try that for the other terms and see if it helps.
Either way, I would try to get rid of the fractions as much as possible. For instance,
[math]\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}[/math] by multiplying top and bottom by x^{2}y^{2}. Try that for the other terms and see if it helps.
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.
Re: Simplify
I get 1
Note that the factor in the bottom right :
[math](\frac{x^2}{y^2}+\frac{y^2}{x^2}2)[/math]
is equal to
[math](\frac{x}{y}\frac{y}{x})^2[/math]
Note that the factor in the bottom right :
[math](\frac{x^2}{y^2}+\frac{y^2}{x^2}2)[/math]
is equal to
[math](\frac{x}{y}\frac{y}{x})^2[/math]
Re: Simplify
Unless x=0 or y=0 or x=y or x=y or x²=y², in which case the whole thing is undefined.
wee free kings
Re: Simplify
I got 2xy/(x^{2} + y^{2}), but I'm very much willing to believe I made a mistake somwhere.

 Posts: 76
 Joined: Mon Mar 05, 2012 12:29 pm UTC
Re: Simplify
Not homework. I found it on a school related forum, but it's unrelated to school.
 Proginoskes
 Posts: 313
 Joined: Mon Nov 14, 2011 7:07 am UTC
 Location: Sitting Down
Re: Simplify
zmic wrote:I get 1
So does Maple.
Re: Simplify
I got this comparatively bizarre answer
[math]\frac{1}{16(x^2+y^2)^2}[/math]
which I suppose could be a bit more elegantly expressed as
[math]\frac{1}{(4x^2+4y^2)^2}[/math]
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.
[math]\frac{1}{16(x^2+y^2)^2}[/math]
which I suppose could be a bit more elegantly expressed as
[math]\frac{1}{(4x^2+4y^2)^2}[/math]
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.

 Posts: 118
 Joined: Tue Jun 24, 2008 2:57 am UTC
 Location: Atlanta, GA
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Re: Simplify
Catmando wrote:I got this comparatively bizarre answer
[math]\frac{1}{16(x^2+y^2)^2}[/math]
which I suppose could be a bit more elegantly expressed as
[math]\frac{1}{(4x^2+4y^2)^2}[/math]
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^21%2Fy^2%29%281%2Fx^21%2Fy^2%29%2F%281%2Fx^2%2B1%2Fy^2%29%29%2F%288%2F%28%28%28x%2By%29%2F%28xy%29%2B%28xy%29%2F%28x%2By%29%29*%28%28x^2%2Fy^2%2By^2%2Fx^22%29%29%29
Re: Simplify
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
[math]\frac{x^4y^4}{4(x^4y^4)^2}[/math]
Thanks!
[math]\frac{x^4y^4}{4(x^4y^4)^2}[/math]
Thanks!
Re: Simplify
In one line, here is the condition which, if met, renders the original form undefined:
x^{5}y = y^{5}x
x^{5}y = y^{5}x
wee free kings
Re: Simplify
Qaanol wrote:In one line, here is the condition which, if met, renders the original form undefined:
x^{5}y = y^{5}x
Hey neat, how'd you combine all the restraints into one equation like that?
Re: Simplify
gfauxpas wrote:Qaanol wrote:In one line, here is the condition which, if met, renders the original form undefined:
x^{5}y = y^{5}x
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 xy=0 or x+y=0 or x²+y²=0
<=>
(x)(y)(xy)(x+y)(x²+y²) = 0
<=>
x^{5}yy^{5}x=0
<=>
x^{5}y = y^{5}x

 Posts: 33
 Joined: Tue Feb 01, 2011 5:57 pm UTC
Re: Simplify
I remember getting that same, exact, obnoxious equation on a math quiz once...
Re: Simplify
benoitowns wrote:I remember getting that same, exact, obnoxious equation on a math quiz once...
And so were you able to solve it?

 Posts: 33
 Joined: Tue Feb 01, 2011 5:57 pm UTC
Re: Simplify
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.
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