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Math Help - Simplifying problem

  1. #1
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    Simplifying problem

    In the equation

    f(x) = -3( (2-3x^2)^-1/2 + 3x^2(2-3x^2)^-3/2)

    my text book jumps to the simplification

    f(x) = -6(2-3x^2)^-3/2)

    Could someone please explain this simplification?
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  2. #2
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    Hello Hefotos
    Quote Originally Posted by Hefotos View Post
    In the equation

    f(x) = -3( (2-3x^2)^-1/2 + 3x^2(2-3x^2)^-3/2)

    my text book jumps to the simplification

    f(x) = -6(2-3x^2)^-3/2)

    Could someone please explain this simplification?
    Note first that:
    (2-3x^2)^{-\frac12}=(2-3x^2)^{-\frac32}\times(2-3x^2)^1
    So we can take out (2-3x^2)^{-\frac32} as a common factor:
    f(x)=-3\Big( (2-3x^2)^{-\frac12} + 3x^2(2-3x^2)^{-\frac32}\Big)
    =-3(2-3x^2)^{-\frac32}\Big( (2-3x^2)^1 + 3x^2\Big)

    =-3(2-3x^2)^{-\frac32}( 2)

    =-6(2-3x^2)^{-\frac32}

    Grandad
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  3. #3
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    Very well explained, thankyou
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