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Math Help - need help with complex rational expression

  1. #1
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    need help with complex rational expression

    1-2/3x
    -----------(fraction line for readabilitys sake)
    x-4/9x

    first thing I do is get the common denominator which is 27x

    I multiply it around and end up with:

    27x - 18/27x^2-12

    then I factor it and end up with

    9(3x-2)/3(9x^2-4)

    the answer is supposed to be

    3/3x+2

    can anyone help me? thanks!
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  2. #2
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    Quote Originally Posted by NecroWinter View Post
    9(3x-2)/3(9x^2-4)

    the answer is supposed to be

    3/3x+2

    can anyone help me? thanks!

    You need to learn the difference of two squares method.

    \displaystyle \frac{9(3x-2)}{3(9x^2-4)}= \frac{9(3x-2)}{3(3x-2)(3x+2)} = \frac{3}{3x+2}
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  3. #3
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    one more quick question only because my book doesnt explain things much

    i have a problem that reads:
    1/x+h - 1/x
    ---------------
    h

    the answer is 1/x(x+h)

    im not sure how to find the common denominator with this one. i assume its x(x+h) but no matter which way i work it it just looks...wrong
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  4. #4
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    \displaystyle \frac{\frac{1}{x+h}-\frac{1}{x}}{h}= \frac{\frac{x-(x+h)}{x(x+h)}}{h}= \frac{1}{h}\times \frac{x-(x+h)}{x(x+h)} =\frac{1}{h}\times\frac{h}{x(x+h)}= \frac{1}{x(x+h)}
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