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Math Help - Simplify

  1. #1
    Newbie
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    Nov 2009
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    Simplify

    Hi

    I need to simplify the following, giving the result without fractional indices:

     \frac{(x^2-1)^2 \sqrt{x+1}}{(x-1)^{3/2}}

    The solution:  (x+1)^2 \sqrt{x^2-1}

    I don't see how they obtain this solution, can somebody give me a few steps?

    Thank you
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  2. #2
    Junior Member
    Joined
    Nov 2009
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    Quote Originally Posted by Coxx View Post
    Hi

    I need to simplify the following, giving the result without fractional indices:

     \frac{(x^2-1)^2 \sqrt{x+1}}{(x-1)^{3/2}}

    The solution:  (x+1)^2 \sqrt{x^2-1}

    I don't see how they obtain this solution, can somebody give me a few steps?

    Thank you
    simplify:
     \frac{(x^2-1)^2 \sqrt{x+1}}{(x-1)^{3/2}}
    ----------------------------------------------------------
    remember:
    (a^2-b^2)=(a-b)(a+b)
    so,
     (x^2-1)^2= ((x-1)(x+1))^2=(x+1)^2 (x-1)^2
    -----------------------------------------------------------
     \frac{(x+1)^2 (x-1)^2 \sqrt{x+1}}{(x-1)^{3/2}}

    u can cancel (x-1)...
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  3. #3
    Super Member

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    May 2006
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    Lexington, MA (USA)
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    Hello, Coxx!

    What a strange way to leave the answer . . .


    Simplify: .  \frac{(x^2-1)^2 \sqrt{x+1}}{(x-1)^{3/2}}

    The solution:  (x+1)^2 \sqrt{x^2-1}

    We have: . \frac{\bigg[(x-1)(x+1)\bigg]^2\sqrt{x+1}}{(x-1)^{\frac{3}{2}}} . = \;\frac{(x-1)^2(x+1)^2(x+1)^{\frac{1}{2}}}{(x-1)^{\frac{3}{2}}}

    . . . . =\; \frac{(x-1)^2}{(x-1)^{\frac{3}{2}}} \cdot\frac{(x+1)^2(x+1)^{\frac{1}{2}}}{1}  \;=\;(x-1)^{\frac{1}{2}}(x+1)^{\frac{1}{2}}(x+1)^2

    . . . . =\;\bigg[(x-1)(x+1)\bigg]^{\frac{1}{2}}(x+1)^2 \;=\;(x^2-1)^{\frac{1}{2}}(x+1)^2

    . . . . = \;\sqrt{x^2-1}\,(x+1)^2

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  4. #4
    Newbie
    Joined
    Nov 2009
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    hi,

    So obvious many thanks

    I just started to improve my maths skills so i'm really a newbie in this field!

    greets
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