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Math Help - Simplifying expressions

  1. #1
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    Simplifying expressions

    1)Simplify for x>0
    sqrt(x^4-4x^2)/x


    i have tried
    sqrt((x+2)(x-2))
    sqrt x^2-4

    but they are incorrect, can anyone help me?

    2) rationalize the denominator and simplify
    x-4/sqrt(x)-4
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  2. #2
    MHF Contributor Reckoner's Avatar
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    Hi lemontea.

    Quote Originally Posted by lemontea View Post
    1)Simplify for x>0
    sqrt(x^4-4x^2)/x


    i have tried
    sqrt((x+2)(x-2))
    sqrt x^2-4

    but they are incorrect, can anyone help me?
    When factoring, you left out an x^2 (Edit: No you didn't; you just canceled it--I'm too tired to read properly). It should be:

    \frac{\sqrt{x^4 - 4x^2}}x

    =\frac{\sqrt{x^2\left(x^2 - 4\right)}}x

    Now, remember that \sqrt{ab} = \sqrt{a}\sqrt{b}, and that \sqrt{a^2} = |a|, and you should be able to simplify this.

    Quote Originally Posted by lemontea View Post
    2) rationalize the denominator and simplify
    x-4/sqrt(x)-4
    I am assuming you mean \frac{x - 4}{\sqrt{x} - 4} and not x - \frac4{\sqrt{x}} - 4 as it is written. If so, please be more careful about your notation in the future.

    Anyway, when rationalizing a binomial denominator, multiply the numerator and denominator of the fraction by the conjugate binomial. For example:

    \frac{a}{\sqrt{2} + \sqrt{3}}

    =\frac{a\color{red}\,\left(\sqrt{2} - \sqrt{3}\right)}{\left(\sqrt{2} + \sqrt{3}\right)\color{red}\left(\sqrt{2} - \sqrt{3}\right)}

    =\frac{a\,\sqrt{2} - a\,\sqrt{3}}{\left(\sqrt{2}\right)^2 + \sqrt{2}\,\sqrt{3} - \sqrt{2}\,\sqrt{3} - \left(\sqrt{3}\right)^2}

    =\frac{a\,\sqrt{2} - a\,\sqrt{3}}{2 - 3}

    =\frac{a\,\sqrt{2} - a\,\sqrt{3}}{-1}

    =a\,\sqrt{3} - a\,\sqrt{2}
    Last edited by Reckoner; May 11th 2008 at 11:34 PM.
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  3. #3
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    1.) I still cant seem to get this question. This is what I did
    sqrt(x^4-4x^2)/x
    =(sqrtx^2(x^2-4))/x
    =(sqrt (x-2)(x+2))

    2.) This is what i got for the
    (sqrt(m)+4)(m-4)/m-16
    but when i submitted it, it's incorrect. What did i do wrong?
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  4. #4
    MHF Contributor Reckoner's Avatar
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    Quote Originally Posted by lemontea View Post
    1.) I still cant seem to get this question. This is what I did
    sqrt(x^4-4x^2)/x
    =(sqrtx^2(x^2-4))/x
    =(sqrt (x-2)(x+2))
    I misread your first post. The answers you got seem correct to me. Have you tried separating the radical into \sqrt{x - 2}\sqrt{x + 2}? I don't see what else you could do here.

    Quote Originally Posted by lemontea View Post
    2.) This is what i got for the
    (sqrt(m)+4)(m-4)/m-16
    but when i submitted it, it's incorrect. What did i do wrong?
    Have you tried multiplying out the numerator? It sounds like you are trying to submit these to an online system, and it is probably very finicky about how your answers are formatted.
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