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    Polynomial Remainder

    Result

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

    Plot

    Plot

    Plot

    Expanded form

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

    Alternate form

    x - 1

    Root

    x = 1

    Properties as a real function

    {x element R : x!=1}

    {y element R : y!=0}

    injective (one-to-one)

    Derivative

    d/dx((1 - 2 x + x^2)/(-1 + x)) = 1

    Indefinite integral

    integral(1 - 2 x + x^2)/(-1 + x) dx = 1/2 (x - 2) x + constant

    Series representation

    (1 - 2 x + x^2)/(-1 + x) = sum_(n=-∞)^∞ ( piecewise | -1 | n = 0 1 | n = 1) x^n

    (1 - 2 x + x^2)/(-1 + x) = sum_(n=-∞)^∞ ( piecewise | 1 | n = 1 0 | otherwise) (-1 + x)^n

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