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Math Help - Algebraic Fractions

  1. #1
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    Algebraic Fractions

    Solve the equation algebraically.

    1. \frac{2x} {x+1} = \frac{x+1} {2}


    2. 6.5 = \frac {52} {sqrt[z]}


    3. 4.3 = sqrt 18 divided by 7
    Last edited by comet2000; August 11th 2008 at 01:22 PM.
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  2. #2
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    For the first one:
    Given: \frac{2x} {x+1} = \frac{x+1} {2}

    Cross Multiply: 2x \cdot 2 = (x+1)\cdot(x+1)

    Simply/expand: 4x = x^2 + 2x + 1

    Subtract 4x from both sides:  0 = x^2 - 2x + 1

    Factor: 0 = (x-1)(x-1) = (x-1)^2

    x = 1

    Can you rewrite the second question?
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  3. #3
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    2. 6.5 = \frac {52} {sqrt[z]}
    the 6.5 = is correct.
    the z is a squareroot.
    52 is on top.
    sorry, still learning the coding for it.
    don't know how to put z in squareroot.
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  4. #4
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    It's better that you write \sqrt{z} instead, not sqrt[z]. If you wanted cube root though, you should write sqrt[3]{z}. The nth root is \sqrt[n]{x} which is \sqrt[n]{x}.

    Given: 6.5 = \frac{52}{\sqrt{z}}
    Multiply by the multiplicative inverse of 6.5 on both sides: 1 = \frac{52}{6.5\sqrt{z}}
    Multiply by \sqrt{z} on both sides: \sqrt{z} = \frac{52}{6.5}
    Square both sides (principal of powers): z = \left(\frac{52}{6.5}\right)^2
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  5. #5
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    Quote Originally Posted by Chop Suey View Post
    It's better that you write \sqrt{z} instead, not sqrt[z]. If you wanted cube root though, you should write sqrt[3]{z}. The nth root is \sqrt[n]{x} which is \sqrt[n]{x}.

    Given: 6.5 = \frac{52}{\sqrt{z}}
    Multiply by the multiplicative inverse of 6.5 on both sides: 1 = \frac{52}{6.5\sqrt{z}}
    Multiply by \sqrt{z} on both sides: \sqrt{z} = \frac{52}{6.5}
    Square both sides (principal of powers): z = \left(\frac{52}{6.5}\right)^2
    hehe, thanks. = me be scare of you.
    what do you mean by "multiplicative inverse"?
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  6. #6
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    If x is a real number (not equal to 0), then the multiplicative inverse of x is \frac{1}{x}

    Don't be scared of me! I'm not really the cookie-monster, hehe.
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