a: ĐKXĐ: \(x \notin \left{\right. 1 ; - 1 ; \frac{1}{2} \left.\right}\)

\(A = \left(\right. \frac{1}{1 - x} + \frac{2}{x + 1} - \frac{5 - x}{1 - x^{2}} \left.\right) : \frac{1 - 2 x}{x^{2} - 1}\)

\(= \left(\right. \frac{- 1}{x - 1} + \frac{2}{x + 1} - \frac{x - 5}{\left(\right. x - 1 \left.\right) \left(\right. x + 1 \left.\right)} \left.\right) \cdot \frac{\left(\right. x - 1 \left.\right) \left(\right. x + 1 \left.\right)}{- 2 x + 1}\)

\(= \frac{- \left(\right. x + 1 \left.\right) + 2 \left(\right. x - 1 \left.\right) - x + 5}{\left(\right. x - 1 \left.\right) \left(\right. x + 1 \left.\right)} \cdot \frac{\left(\right. x - 1 \left.\right) \left(\right. x + 1 \left.\right)}{- 2 x + 1}\)

\(= \frac{- x - 1 + 2 x - 2 - x + 5}{- 2 x + 1} = \frac{2}{- 2 x + 1}\)

b: Để A>0 thì \(\frac{2}{- 2 x + 1} > 0\)

mà 2>0

nên -2x+1>0

=>-2x>-1

=>\(x < \frac{1}{2}\)

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