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Math Help - precal help

  1. #1
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    precal help

    simplify: (x-(1/x^2))/(x-(1/x^3))

    simplify: 4+___d___
    4+_4_
    4+d
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  2. #2
    MHF Contributor
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    I'm not quite sure what the second question says, but for the first question you'll be needing common denominators. Working on the numerator first, we have x - \frac{1}{x^2}. To get a common denominator, multiply x \cdot \frac{x^2}{x^2} so that you get \frac{x^3}{x^2} - \frac{1}{x^2}. Subtracting yields \frac{x^3 - 1}{x^2}. Can you simplify the denominator?
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  3. #3
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    the bottom one, with many parantheses, says 4+(d/(4+(4/(4+d))))
    i simplified the bottom part, but what do i do next?
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  4. #4
    MHF Contributor
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    For the first question, you should have gotten \frac{x^4 - 1}{x^3} as the denominator, which leaves you with \frac{\frac{x^3 - 1}{x^2}}{\frac{x^4 - 1}{x^3}}. Now, you can rearrange this (using the reciprocal rule) to \frac{x^3(x^3 - 1)}{x^2(x^4 - 1)}. You can cancel out x^2 in the top and bottom to yield \frac{x(x^3 - 1)}{x^4 - 1} and then remove a factor of x-1 from both top and bottom to yield \frac{x(x^2 + x + 1)}{x^3 + x^2 + x + 1} and that's as simplified as it gets.

    For the second question, using the parentheses, work from the inside out, using common denominators to combine fractions.
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