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Math Help - Rationalizing the Numerator

  1. #1
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    Rationalizing the Numerator

    1) 1/(Square Root of x) - 1 / x - 1

    So I multiply both top and bottom by 1/(Square Root of x) + 1 , right? But I don't know what that equals, I just don't know how to multiply them...

    2) x(Square Root of x) - 8 / x - 4

    Same thing...maybe if I get help on 1 I can get this one.

    More questions to come I'm sure...
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Dickson View Post
    1) 1/(Square Root of x) - 1 / x - 1



    So I multiply both top and bottom by 1/(Square Root of x) + 1 , right? But I don't know what that equals, I just don't know how to multiply them...



    2) x(Square Root of x) - 8 / x - 4



    Same thing...maybe if I get help on 1 I can get this one.



    More questions to come I'm sure...
    If you typed more intelligibly, it would be easier t answer you and you would have probably gotten an answer by now.

    what you typed can be interpreted several ways, please use parentheses to clarify

    i believe the first question is \frac {\frac 1{\sqrt{x}} - 1}{x - 1}. personally, i'd combine the fractions first, but multiplying by \frac { \frac 1{\sqrt{x}} + 1}{ \frac 1{\sqrt{x}} + 1} is a valid option.

    note that the whole point of multiplying by the conjugate is to obtain the difference of two squares. hence the numerator will change from the form (x - y)(x + y) to the form x^2 - y^2, and we get

    \frac {\frac 1x - 1}{(x - 1) \left( \frac 1{\sqrt{x}} + 1\right)}

    now simplify


    for the second problem, note that you have \frac {(x^{1/2})^3 - 8}{x - 4}

    which should remind you of the difference of two cubes formula, which should help you know how to proceed.
    Last edited by mr fantastic; February 1st 2009 at 05:51 PM. Reason: Moderation
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  3. #3
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    Quote Originally Posted by Dickson View Post
    1) 1/(Square Root of x) - 1 / x - 1

    So I multiply both top and bottom by 1/(Square Root of x) + 1 , right? But I don't know what that equals, I just don't know how to multiply them...

    2) x(Square Root of x) - 8 / x - 4

    Same thing...maybe if I get help on 1 I can get this one.

    More questions to come I'm sure...
    Note that the key is knowing the formula: (a+b)(a-b)=a^2-b^2

    \frac{\frac{1}{\sqrt{x}}-1}{x-1} \times \frac{\frac{1}{\sqrt{x}}+1}{\frac{1}{\sqrt{x}}+1}=  \frac{\frac{1}{x}-1}{(x-1)(\frac{1}{\sqrt{x}}+1)}=...
    See if you can take it from here.
    Last edited by chabmgph; February 1st 2009 at 04:46 PM. Reason: Too slow.
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  4. #4
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    yeah i got tha ...i don't know how to multiply the 2 binomials
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