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Thread: Fractions and equations.

  1. February 3rd 2009, 09:58 AM #1
    Pingu
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    Fractions and equations.

    Im having a little trouble with this one:

    <br /> \frac{3}{x-2}-\frac{2}{x+3}=\frac{2}{5}<br />

    I can't find a decent "bottom half" fraction for this. Im thinking

    <br /> 5(x-2)(x+3)<br />
    Last edited by ThePerfectHacker; February 3rd 2009 at 10:20 AM.
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  2. February 3rd 2009, 10:17 AM #2
    Bruce
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    Quote Originally Posted by Pingu View Post
    Im having a little trouble with this one:

    <br /> \frac{3}{x-2}-\frac{2}{x+3}=\frac{2}{5}<br />

    I can't find a decent "bottom half" fraction for this. Im thinking

    <br /> 5(x-2)(x+3)<br />
    Your denominator is good. Now set that as your denominator for each fraction. You will then have to multiply the top by the same thing you multiplied the bottom by. So:

    \frac {3 * 5(x+3)}{5(x - 2)(x + 3)} - \frac {2 * 5(x -2)}{5(x-2)(x+3)} = \frac {2 * (x-2)(x+3)}{5(x-2)(x+3)}

    then you simplify:

    \frac {15x + 45}{5(x-2)(x+3)} - \frac {10x - 20}{5(x-2)(x+3)} = \frac {2x^2 + 2x - 12}{5(x-2)(x+3)}

    Do the subtracting...

    \frac {5x + 65}{5(x-2)(x+3)} = \frac {2x^2 + 2x - 12}{5(x-2)(x+3)}

    Multiply both sides by the same denominator...

    5x + 65 = 2x^2 + 2x - 12

    Can you do it from here?
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  3. February 3rd 2009, 10:20 AM #3
    Pingu
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    Yes, I've tried that, and it turns out pretty messy. The correct number for X is 7, If my calculator is correct.
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  4. February 3rd 2009, 10:22 AM #4
    topher0805
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    Quote Originally Posted by Pingu View Post
    Yes, I've tried that, and it turns out pretty messy. The correct number for X is 7, If my calculator is correct.
    It shouldn't be messy. You just need to get it into quadratic form and use this formula:

    x = \frac{-b \pm \sqrt{b-4ac}}{2a}
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  5. February 3rd 2009, 10:24 AM #5
    Pingu
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    [quote=topher0805;
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  6. February 3rd 2009, 10:31 AM #6
    hkerbest
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    <br /> -2x^2 + 3x = - 77<br />

    <br /> (-2x+3)(x-0) = - 77<br />



    X = 7 X = -5,5
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