Question

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Answer 1

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$\frac{x-x^2}{x^2-1} \div( \frac{x}{x+1} -x)= \\ \\ \frac{x-x^2}{x^2-1} \div[ \frac{x-x(x+1)}{x+1} ]= \\ \\ \frac{x-x^2}{x^2-1} \div( \frac{x-x^2-x}{x+1} )= \\ \\ \frac{x(1-x)}{(x+1)(x-1)} \times \frac{x+1}{-x^2} = \\ \\ \frac{-x(x-1)}{(x+1)(x-1)} \times \frac{x+1}{-x^2} = \\ \\ cancelar \\ \\ \frac{-x}{-x^2} = \frac{1}{x}$