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Math Help - why are these equal?

  1. #1
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    why are these equal?

    my text says that


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

    is equal to



    (x-3)^(-1/2) [2 (x-3) - x ]
    --------------------------------
    x- 3


    but where did the 1/2 exponent for (x-3) go?
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  2. #2
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    Re: why are these equal?

    Quote Originally Posted by kingsolomonsgrave View Post
    my text says that


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

    is equal to

    (x-3)^(-1/2) [2 (x-3) - x ]
    --------------------------------
    x- 3
    What does y^{-1/2}(y-1)=~?
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  3. #3
    Super Member ILikeSerena's Avatar
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    Re: why are these equal?

    Hi kingsolomonsgrave!

    Suppose we only look at the nominator to keep things simple.
    And suppose we define y=(x-3)^{1/2}.
    Then this implies that y^{-1}=(x-3)^{-1/2} (do you know why?).
    It also implies that y^2 = (x-3).

    If we substitute these into your first nominator, you'll get:
    2 y - x y^{-1}

    And if we substitute them into your second nominator, you'll get:
    y^{-1} [ 2 y^2 - x ]

    Can you see that those expressions are identical?
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