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"rationalize" the denominator rather than the numerator

  1. May 8, 2005 #1
    Hello All

    I get to thrown off when there is a question with radicals . Can you please help

    Simplify the following

    [tex]\frac{\sqrt{x} + 1}{\sqrt{x} - 1}[/tex]


    and Preform the indicated operations and simplfy


    [tex]\sqrt{x}(\sqrt{x} + 1)(2\sqrt{x}-1)[/tex]

    Thanks

    P
     
  2. jcsd
  3. May 8, 2005 #2
    the first:

    [tex]\frac{\sqrt{x} + 1}{\sqrt{x} - 1}[/tex]

    [tex]\frac{(\sqrt{x} + 1)(\sqrt{x} - 1)}{(\sqrt{x} - 1)(\sqrt{x} - 1)}[/tex]

    [tex]\frac{x-1}{x -2 \sqrt{x} +1}[/tex]

    the second:

    [tex]\sqrt{x}(\sqrt{x} + 1)(2\sqrt{x}-1)[/tex]

    [tex]\sqrt{x}(2x+ \sqrt{x}-1)[/tex]

    [tex]2x \sqrt{x}+x- \sqrt{x}[/tex]
     
  4. May 8, 2005 #3

    HallsofIvy

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    I would have been inclined to "rationalize" the denominator rather than the numerator:
    [tex]\frac{\sqrt{x}+1}{\sqrt{x}-1}= \frac{(\sqrt{x}+1)(\sqrt{x}+1)}{(\sqrt{x}-1})(\sqrt{x}+1)}= \frac{x+ 2\sqrt{x}+1}{x-1}[/tex]
     
  5. May 8, 2005 #4
    thanks thats the answers I got but was not sure

    When would you "rationalize" the denominator over the numerator or the other way around.
     
  6. May 8, 2005 #5
    Generally simplified form means always "rationalizing" the denominator. Also you can simplify a little bit more. [tex] \frac{x+ 2\sqrt{x}+1}{x-1} = \frac{ (1+\sqrt{x})^2}{x-1}[/tex]
     
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