Đáp án:
Giải thích các bước giải:
$a) A = \bigg(\dfrac{\sqrt{a} + 1}{\sqrt{a} - 1}-\dfrac{\sqrt{a} - 1}{\sqrt{a} + 1}\bigg) . \dfrac{a - 1}{4(a + 1)} \\=\dfrac{(\sqrt{a} + 1)^2 - (\sqrt{a} - 1)^2}{(\sqrt{a} - 1 )(\sqrt{a} + 1)} . \dfrac{a - 1}{4(a + 1)}\\=\dfrac{a + 2\sqrt{a} + 1 - a + 2\sqrt{a}}{a - 1} . \dfrac{a - 1}{4(a + 1)}\\ = \dfrac{4\sqrt{a}}{a - 1} . \dfrac{a - 1}{4(a + 1)} \\=\dfrac{\sqrt{a}}{a + 1} \\ b)B = \bigg( \dfrac{\sqrt{x}}{\sqrt{x} + 1} + \dfrac{\sqrt{x}}{\sqrt{x} - 1}\bigg)\bigg(\sqrt{a} - \dfrac{1}{2}\bigg)\\ = \dfrac{\sqrt{x}(\sqrt{x} - 1) + \sqrt{x}(\sqrt{x} + 1)}{(\sqrt{x} + 1)(\sqrt{x} - 1)} . \dfrac{x\sqrt{x} - 1}{x}\\ = \dfrac{x - \sqrt{x} + x + \sqrt{x}}{(\sqrt{x} + 1)(\sqrt{x} - 1)} . \dfrac{(\sqrt{x} - 1)(x + \sqrt{x} + 1)}{x}\\= \dfrac{2x}{(\sqrt{x} + 1)(\sqrt{x} - 1)} . \dfrac{(\sqrt{x} - 1)(x + \sqrt{x} + 1)}{x}\\ = \dfrac{2(x + \sqrt{x} + 1)}{\sqrt{x} + 1}\\ c) C = \bigg(\dfrac{1}{\sqrt{x} - 1} - \dfrac{1}{\sqrt{x} + 1}\bigg) . \dfrac{x - 1}{x}\\ = \dfrac{\sqrt{x} + 1 - \sqrt{x} + 1}{(\sqrt{x} + 1)(\sqrt{x} - 1)} . \dfrac{x - 1}{x}\\ = \dfrac{2}{x - 1} . \dfrac{x - 1}{x} \\ = \dfrac{2}{x}$
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