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Math question - dividing polynomials?

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How do you solve this?

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

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  1. 9-x^(-2) / 3+x^(-1)=

    (9-1/x^2)/(3+1/x)=

    [(9x^2-1)/x^2]/[(3x+1)/x]=

    (9x^2-1)/x^2 * x/(3x+1)=

    (3x+1)(3x-1)/x^2 * x/(3x+1)=

    (3x-1)/x

    (3x-1)/x=0 (?)

    3x-1=0

    x=1/3

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