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Math Help - express the fraction in simplest form

  1. #1
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    express the fraction in simplest form

    (1+(1/(x^2-1)))/((1/x)-(x/(x+1)))
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  2. #2
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    Start by making common denominators in both top and bottom of the fraction. You follow?
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  3. #3
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    yup i did do that. the answer i got was x^3/(-x^3+2x^2-x-1) but the answer sheet says its x^3/(-x^3+2x^2-1)
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  4. #4
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    Thank you for using brackets, but this is still very hard to read...

    Is it \frac{1 + \frac{1}{x^2 - 1}}{\frac{1}{x} - \frac{x}{x + 1}}?

    If so, start by making some common denominators

    \frac{1 + \frac{1}{x^2 - 1}}{\frac{1}{x} - \frac{x}{x + 1}} = \frac{\frac{x^2 - 1}{x^2 - 1} + \frac{1}{x^2 - 1}}{\frac{x + 1}{x(x + 1)} - \frac{x^2}{x(x + 1)}}

     = \frac{\frac{x^2}{x^2 - 1}}{\frac{-x^2 + x + 1}{x(x + 1)}}

     = \frac{\frac{x^2}{(x - 1)(x + 1)}}{\frac{-x^2 + x + 1}{x(x + 1)}}

     = \frac{x^3(x + 1)}{(x - 1)(x + 1)(-x^2 + x + 1)}

     = \frac{x^3}{(x - 1)(-x^2 + x + 1)}.
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  5. #5
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    yup i've got it now. thanks!
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