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## #1 2005-05-13 09:34:40

im really bored
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### Algebra help

I'm having trouble doing this problem:

solve for x

(square root of ( x + 1) + (square root of (x - 1)        4x - 1
_________(divided by)_____________________   =  ___(divided by)___
(square root of ( x + 1) - (square root of (x - 1)             (2)

## #2 2005-05-13 09:54:16

MathsIsFun

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### Re: Algebra help

I will work on it ...

I think the trick will be to multiply by [sqrt(x+1)-sqrt(x-1)]^2

Anyway, let's try and see how far we get

[sqrt(x+1)-sqrt(x-1)] * [sqrt(x+1)+sqrt(x-1)] =  [sqrt(x+1)-sqrt(x-1)]^2 * (4x-1)/2

sqrt(x+1) * sqrt(x+1) + sqrt(x+1) * sqrt(x-1) - sqrt(x-1) * sqrt(x-1) - sqrt(x-1) * sqrt(x-1) = ...

(x+1) + (terms cancel each other) - (x-1) = ...

2 =  [sqrt(x+1)-sqrt(x-1)] *  [sqrt(x+1)-sqrt(x-1)] *  (4x-1)/2

2 = [sqrt(x+1) * sqrt(x+1) - sqrt(x+1) * sqrt(x-1) - sqrt(x-1) * sqrt(x+1) + sqrt(x-1) * sqrt(x-1)] *  (4x-1)/2

2 = [(x+1) - 2 * sqrt(x+1) * sqrt(x-1) + (x-1)]  * (4x-1)/2

2 = [2x - 2 * sqrt(x+1) * sqrt(x-1) ] * (4x-1) / 2

4 = [2x - 2 * sqrt(x+1) * sqrt(x-1) ] * (4x-1)

Hmmm ... that helped a bit, let's try it again but using [sqrt(x+1)+sqrt(x-1)] * [sqrt(x+1)-sqrt(x-1)]

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #3 2005-05-13 10:30:52

MathsIsFun

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### Re: Algebra help

For simplicity, let's call sqrt(x+1) "A" and sqrt(x-1) "B"

You have: (A+B)/(A-B) = (4x-1)/2

Multiply both sides by (A+B)*(A-B):    (A+B)*(A-B) * (A+B)/(A-B) = (A+B)*(A-B) *  (4x-1)/2

Cancel: (A+B)^2 = (A+B)*(A-B) *  (4x-1)/2

Expand: A^2 + 2AB + B^2 = (A^2 - B^2) * (4x-1)/2

Substitute A^2 = (x+1) and B^2 = (x-1): (x+1) + 2AB + (x-1) = ((x+1) - (x-1)) * (4x-1)/2

Simplify: 2x + 2AB = 2 * (4x-1)/2

More: 2x + 2AB = 4x - 1

More: 2AB = 2x - 1

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #4 2005-05-13 10:33:45

im really bored
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### Re: Algebra help

Wow it makes alot more sense putting it that way, I was tying to aproach it from some other way, which turned out horrible.Thanks for the help I understand it now

Last edited by im really bored (2005-05-13 10:42:09)

## #5 2005-05-13 10:41:38

MathsIsFun

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### Re: Algebra help

Well, we still aren't ALL the way there ... we still have 2AB to solve

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #6 2005-05-13 10:44:13

im really bored
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### Re: Algebra help

I know, but i can handle that.  It was just my approach that was getting me. I was trying to go at it in a more complicated way

## #7 2005-05-13 10:45:49

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### Re: Algebra help

Cool ... I will leave it for someone else then ...

Good luck.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #8 2005-05-13 20:20:21

Milos
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### Re: Algebra help

2AB = 2x - 1  ^2
4A^2B^2=4x^2 - 2x + 1
Now: A=sqr(x+1); B=sqr(x-1)
4x^2-4=4x^2 - 4x + 1
then:
4x=5
x=5/4
It was easy, because administrator has finished the difficult part.

## #9 2005-05-13 20:50:01

MathsIsFun

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### Re: Algebra help

Thanks, Milos ...

TEAMWORK !

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Milos
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n e time