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Math Help - Need help figuring out index law question .. stuck .. please help

  1. #1
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    Need help figuring out index law question .. stuck .. please help

    hey guys theres this one question ive been working on forever ..

    its an index law question




    it asks to simplify it

    i understand anything rooted is to the power of a half and i am absolutely clueless as to how to advance in this question .. everything else i can do fin except this one question

    thanks guys ..

    BTW the back of book answer is : x(x-1)^-0.5
    Attached Thumbnails Attached Thumbnails Need help figuring out index law question .. stuck .. please help-maths.bmp  
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  2. #2
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    Quote Originally Posted by jimzer View Post
    hey guys

    ive been working on this question for more than a day and i can do all others except this single one ..

    simplify : <refer to attachment>

    i understand anything rooted is to the power of negative 1/2 but i seriously cannot figure this question out ..

    the back of book answers is : x(x-1)^0.5

    thanks a lot guys
    Get a common denominator:

    \frac{1}{\sqrt{x-1}} + \sqrt{x-1} = \frac{1}{\sqrt{x-1}} + \frac{\sqrt{x-1} \cdot \sqrt{x-1}}{\sqrt{x-1}}


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


    = \frac{x}{\sqrt{x-1}} = \frac{x}{(x-1)^{1/2}} = x (x-1)^{-1/2}.

    The book's answer is wrong.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Get a common denominator:

    \frac{1}{\sqrt{x-1}} + \sqrt{x-1} = \frac{1}{\sqrt{x-1}} + \frac{\sqrt{x-1} \cdot \sqrt{x-1}}{\sqrt{x-1}}


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


    = \frac{x}{\sqrt{x-1}} = \frac{x}{(x-1)^{1/2}} = x (x-1)^{-1/2}.

    The book's answer is wrong.
    thank you so much man, just gotta figure it out now!!

    and i wrote the wrong answer down its actually ^-0.5

    thanks so much again, and sry for double posting
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