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Math Help - Simplifying an Expression with negative exponents

  1. #1
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    Jun 2009
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    Unhappy Simplifying an Expression with negative exponents

    -x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2
    --------------------------------------
    x^4




    This is what I've been doing


    -x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2 x (1-x^2)^1/2
    --------------------------------------
    x^4 x (1-x^2)^1/2


    -x^3-2x(1-x^2)
    ------------------
    x^4 <--------------- This is the part I'm stuck on!!!

    How do you continue working this problem?? Thanks in advance for the help!!
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  2. #2
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    Quote Originally Posted by tarabshort View Post
    -x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2
    --------------------------------------
    x^4




    This is what I've been doing


    -x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2 x (1-x^2)^1/2
    --------------------------------------
    x^4 x (1-x^2)^1/2


    -x^3-2x(1-x^2)
    ------------------
    x^4 <--------------- This is the part I'm stuck on!!!

    How do you continue working this problem?? Thanks in advance for the help!!
    See your last step,

     =\frac{-x^3-2x(1-x^2)}{x^4(1-x^2)^{\frac{1}{2}}}

     =\frac{-x^3-2x+2x^3}{x^4(1-x^2)^{\frac{1}{2}}}

     =\frac{x^3-2x}{x^4(1-x^2)^{\frac{1}{2}}}

     =\frac{x(x^2-2)}{x^4(1-x^2)^{\frac{1}{2}}}

     =\frac{x^2-2}{x^3(1-x^2)^{\frac{1}{2}}}

     =\frac{x^2-2}{x^3\sqrt{1-x^2}}
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Detroit, MI
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    Quote Originally Posted by tarabshort View Post
    -x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2
    --------------------------------------
    x^4




    This is what I've been doing


    -x^3(1-x^2)^-1/2 - 2x(1-x^2)^1/2 x (1-x^2)^1/2
    --------------------------------------
    x^4 x (1-x^2)^1/2


    -x^3-2x(1-x^2)
    ------------------
    x^4 <--------------- This is the part I'm stuck on!!!

    How do you continue working this problem?? Thanks in advance for the help!!
    Always factor out the LEAST common factor. That includes negative exponents. So, what's bigger. 1/2 or -1/2.

    Check it out.

    Factoring out x(1-x^2)^{-1/2} gives

    \frac{x(1-x^2)^{-1/2}[-x^2-2(1-x^2)]}{x^4}

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

    =-\frac{2}{x^3\sqrt{1-x^2}}
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