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AP Calc.

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Simplify:

[(x^-3)-x]/[(x^-2)-1]

  • AP Calc. -

    x^3-x = x(x^2-1)

  • AP Calc. -

    I don't get it...

  • AP Calc. -

    sure you do. factor out x^2-1 top and bottom

  • AP Calc. -

    but don't you have to get rid of the negative exponents somehow..?

  • AP Calc. -

    sorry. I missed the negative exponents.

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

    (1 - x^4)/x^3 / (1-x^2)/x^2

    (1-x^4)/x^3 * x^2/(1-x^2)

    (1-x^2)(1+x^2) / x(1-x^2)

    (1+x^2)/x

  • AP Calc. -

    How did you go from the original question to the 1st step?

  • AP Calc. -

    1/x^3 - x

    over a common denominator of x^3, x = x^4/x^3

  • AP Calc. -

    ohmygosh.. i'm an idiot.. thank you! you're the bestt!(:

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