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Math Help - please help

  1. #1
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    Exclamation please help

    please help me

    express with rational denominator

    1 / 1 + √3 + √5 + √15

    and expand:

    (√x -1 + 1/√x)^2
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  2. #2
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    Re: please help

    Quote Originally Posted by richardkim4668 View Post
    please help me
    express with rational denominator

    1 / 1 + √3 + √5 + √15

    and expand:

    (√x -1 + 1/√x)^2
    need to ask you to wrap things in parentheses to make things clear. do you mean

    $\dfrac 1 {1+\sqrt{3}+\sqrt{5}+\sqrt{15}}$ ?

    for the second one

    $(\sqrt{x}-1+\dfrac 1 {\sqrt{x}})^2 =$

    $(\sqrt{x})^2-\sqrt{x}+\sqrt{x}\dfrac 1 {\sqrt{x}} - \sqrt{x} + 1 - \dfrac 1 {\sqrt{x}} + \dfrac 1 {\sqrt{x}} \sqrt{x} - \dfrac 1 {\sqrt{x}} + \left(\dfrac 1 {\sqrt{x}}\right)^2=$

    $x - 2\sqrt{x} + 3 - \dfrac 2 {\sqrt{x}} + \dfrac 1 x=$

    $\dfrac {x^2 - 2x^{3/2} + 3x - 2\sqrt{x} + 1} x$
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  3. #3
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    Re: please help

    yup i mean that
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  4. #4
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    Re: please help

    Quote Originally Posted by romsek View Post
    need to ask you to wrap things in parentheses to make things clear. do you mean

    $\dfrac 1 {1+\sqrt{3}+\sqrt{5}+\sqrt{15}}$ ?
    Quote Originally Posted by richardkim4668 View Post
    yup i mean that
    $\dfrac 1 {1+\sqrt{3}+\sqrt{5}+\sqrt{15}}=$

    $\dfrac 1 {1+\sqrt 3 + \sqrt 5(1 + \sqrt 3)} = $

    $\dfrac 1 {(\sqrt 3 + 1)(\sqrt 5 + 1)} = $

    $\dfrac 1 {(\sqrt 3 + 1)(\sqrt 5 + 1)}\dfrac{\sqrt 5 - 1}{\sqrt 5 - 1}=$

    $\dfrac{\sqrt 5 - 1}{(\sqrt 3 +1)(4)}=$

    $\dfrac{\sqrt 5 - 1}{(\sqrt 3 +1)(4)}\dfrac{\sqrt 3 -1}{\sqrt 3 - 1}=$

    $\dfrac{(\sqrt 5 - 1)(\sqrt 3 - 1)}{(2)(4)}=$

    $\dfrac{(\sqrt 5 - 1)(\sqrt 3 - 1)} 8$

    $\dfrac {\sqrt {15} - \sqrt 3 - \sqrt 5 + 1} 8$
    Last edited by romsek; April 10th 2014 at 04:56 AM.
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