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Thread: Simplify and Rationalize

  1. #1
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    Simplify and Rationalize

    Question: For x>0, simplify the following:
    $\displaystyle
    \sqrt{x^4-4x^2}/x
    $

    Hint: If x<0, what is :
    $\displaystyle
    \sqrt{x^2}
    $
    Last edited by mvho; May 22nd 2009 at 04:05 PM.
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  2. #2
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    Quote Originally Posted by mvho View Post
    3). Rationalise the denominator, then simplify:m-4/ sq. root m-4

    My Answer:

    I take the conjugate which is : sq. root m +4, so my denominator ends up being just m-4. Is my top: Sq root m -16?

    So:

    Sq. Root m-16/m-4?
    Thannks!
    No, rationalizing the denominator doesn't mean multiplying by a conjugate. You just multiply the numerator & denominator by the denominator itself:
    $\displaystyle \frac{m-4}{\sqrt{m-4}}$

    $\displaystyle \frac{m-4}{\sqrt{m-4}}*\frac{\sqrt{m-4}}{\sqrt{m-4}}$

    $\displaystyle \frac{(m-4)\sqrt{m-4}}{m-4}$

    $\displaystyle \sqrt{m-4}$

    I didn't do #1 or #2 because I couldn't figure out what your problems were. Can you use the math tags or put in some parentheses?


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  3. #3
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    Er i am assuming that the square root applies to only $\displaystyle x^4$

    1.$\displaystyle \frac{\sqrt (x^4)-(4x^2)}{x}$

    $\displaystyle \frac{(x^2)-(4x^2)}{x}$

    $\displaystyle x-(4x)$

    $\displaystyle -3x$

    lol think so
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  4. #4
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    Hmm... The square root for question #3, ends at the m. Ill have to find out how to use math tags.

    Any links to learn how to use math tags? I need that sq. root symbol!
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  5. #5
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    Quote Originally Posted by mvho View Post
    Hmm... The square root for question #3, ends at the m. Ill have to find out how to use math tags.
    Please do! So you mean
    $\displaystyle \frac{m - 4}{\sqrt{m} - 4}$?
    Then yes, you would multiply by the conjugate:
    $\displaystyle \frac{m - 4}{\sqrt{m} - 4} * \frac{\sqrt{m} + 4}{\sqrt{m} + 4}$
    $\displaystyle \frac{(m - 4)(\sqrt{m} + 4)}{(\sqrt{m})^{2} - 4^{2}}$
    $\displaystyle \frac{(m - 4)(\sqrt{m} + 4)}{m - 16}$
    Dunno if it's necessary to FOIL the numerator. There's nothing else to simplify that I can see.


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  6. #6
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    yeongil: Thats right. That is what I got too. How do yo use these math tags though? Is there a FAQ somewhere?
    Er i am assuming that the square root applies to only

    The square root applies to the entire numerator. I need to learn about these math tags!!
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  7. #7
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    Quote Originally Posted by mvho View Post
    yeongil: Thats right. That is what I got too. How do yo use these math tags though? Is there a FAQ somewhere?



    The square root applies to the entire numerator. I need to learn about these math tags!!
    http://www.mathhelpforum.com/math-he...-tutorial.html

    the file attached there should explain everything.
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  8. #8
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    Thanks for the link! I have revised my question now, so it Should be much clearer.

    I am unclear what the hint is implying, does anyone have a clue?

    Here is my answer:

    $\displaystyle
    -\sqrt{x^2-4}
    $



    I know I can simplify further (difference of squares) but this looks neater and I m done fooling around with latex for 1 day
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