` a) ` ` A = (\frac{1}{x + 1} - \frac{1}{x^2 - 1}) . \frac{x + 1}{x - 2} `
` A = (\frac{1}{x + 1} - \frac{1}{(x - 1)(x + 1)}) . \frac{x + 1}{x - 2} `
` A = \frac{x - 1 - 1}{(x - 1)(x + 1)} . \frac{x + 1}{x - 2} `
` A = \frac{x - 2}{x - 1} . \frac{1}{x - 2} `
` A = \frac{1}{x - 1} . 1 `
` A = \frac{1}{x - 1} `
Vậy ` A = \frac{1}{x - 1} `
` b) ` Để ` A < 0 ` thì:
` \frac{1}{x - 1} < 0 `
Vì ` 1 > 0 `
` => x - 1 < 0 `
` <=> x < 1 `
Vậy ` x < 1 ` thì ` A < 0 `