## Simplify

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

Annihilist
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.

z4lis
Posts: 767
Joined: Mon Mar 03, 2008 10:59 pm UTC

### Re: Simplify

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.
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.

zmic
Posts: 419
Joined: Fri Mar 02, 2012 10:38 pm UTC

### Re: Simplify

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
The Cheshirest Catamount
Posts: 3054
Joined: Sat May 09, 2009 11:55 pm UTC

### 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

Nyktos
Posts: 138
Joined: Mon Mar 02, 2009 4:02 pm UTC

### Re: Simplify

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

Annihilist
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.

Catmando
Posts: 47
Joined: Fri Nov 19, 2010 9:48 pm UTC

### Re: Simplify

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
Posts: 118
Joined: Tue Jun 24, 2008 2:57 am UTC
Location: Atlanta, GA
Contact:

### Re: Simplify

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

Catmando
Posts: 47
Joined: Fri Nov 19, 2010 9:48 pm UTC

### 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

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

Thanks!

Qaanol
The Cheshirest Catamount
Posts: 3054
Joined: Sat May 09, 2009 11:55 pm UTC

### Re: Simplify

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

x5y = y5x
wee free kings

gfauxpas
Posts: 97
Joined: Sun Oct 09, 2011 11:24 pm UTC
Contact:

### Re: Simplify

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?

Tirian
Posts: 1891
Joined: Fri Feb 15, 2008 6:03 pm UTC

### Re: Simplify

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

benoitowns
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...

Afif_D
Posts: 184
Joined: Wed Oct 06, 2010 2:56 pm UTC

### 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?

benoitowns
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.