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Compute the derivative of a given function

Compute the derivative of

    \[ f(x) = \frac{1+x-x^2}{1-x+x^2}. \]


Using the quotient rule for the derivative, we compute

    \[ f'(x) = \frac{(1 -2x)(1-x+x^2) - (1+x-x^2)(-1+2x)}{(1-x+x^2)^2} = \frac{2(1-2x)}{(1-x+x^2)^2}. \]

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