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Math Help - Need algebra to simplify/solve an equation

  1. #1
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    Need algebra to simplify/solve an equation

    the equation that i need to simplify first is ((x^2-1)^1/2 -(x^2-1)^-1/2 (2-x^2)) / (x^2-1)= 0

    after i move the negative power, im not exactly sure what to do. I would multiply by the reciprical to get rid of the fration in the numerator but the 1/2 exponent makes things difficult. help is much appreciated!
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  2. #2
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    Re: Need algebra to simplify/solve an equation

    Do you mean simplify or solve?

    Is this the equation?

    \displaystyle \frac{ \frac{1}{\sqrt{x^2-1}} - \frac{(2-x^2)}{\sqrt{x^2-1}}  }{x^2-1} = 0

    if so, x\neq 1,-1

    \displaystyle \frac{ \frac{1- (2-x^2)}{\sqrt{x^2-1}}   }{x^2-1} = 0

    \displaystyle \frac{ \frac{1- 2+x^2}{\sqrt{x^2-1}}   }{x^2-1} = 0

    \displaystyle \frac{ \frac{-1+x^2}{\sqrt{x^2-1}}   }{x^2-1} = 0

    Now you can multiply both sides by x^2-1

    \displaystyle  \frac{-1+x^2}{\sqrt{x^2-1}}    = 0

    Multiply both sides by \sqrt{x^2-1} and you'll find x=1,-1 , but can it?
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  3. #3
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    Re: Need algebra to simplify/solve an equation

    Edit: Wrong Post...
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  4. #4
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    Re: Need algebra to simplify/solve an equation

    yes thats basically the right equation. the answer key says the answer is x = plus or minus the squareroot of 3/2. and i have no idea how that can work out...
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  5. #5
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    Re: Need algebra to simplify/solve an equation

    I think the correct interpretation is:

    \dfrac{\sqrt{x^2-1}-\dfrac{2-x^2}{\sqrt{x^2-1}}}{x^2-1}=0

    \dfrac{\dfrac{(\sqrt{x^2-1})^2-(2-x^2)}{\sqrt{x^2-1}}}{x^2-1}=0

    \dfrac{x^2-1-2+x^2}{\sqrt{x^2-1}(x^2-1)}=0

    \dfrac{2x^2-3}{\sqrt{x^2-1}(x^2-1)}=0

    Which is 0 if

    2x^2-3=0 \Rightarrow x=\pm \sqrt{\dfrac{3}{2}}
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  6. #6
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    Re: Need algebra to simplify/solve an equation

    Quote Originally Posted by Victalam View Post
    yes thats basically the right equation....
    basically?
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