Cho biểu thức: A=(√a/√a+1−√a/√a−1+2√a−4/a−1):1√a+1 ( a ≥ 0; a≠1). Rút gọn biểu thức A .

ĐKXĐ : \[a \ge 0,a \ne 1\]

\[A = \left[ {\frac{{\sqrt a (\sqrt a - 1)}}{{\left( {\sqrt a + 1} \right)\left( {\sqrt a - 1} \right)}} - \frac{{\sqrt a \left( {\sqrt a + 1} \right)}}{{\left( {\sqrt a + 1} \right)\left( {\sqrt a - 1} \right)}} + \frac{{2\sqrt a - 4}}{{\left( {\sqrt a + 1} \right)\left( {\sqrt a - 1} \right)}}} \right].\left( {\sqrt a + 1} \right)\]

\[A = \frac{{a - \sqrt a - a - \sqrt a + 2\sqrt a - 4}}{{\left( {\sqrt a + 1} \right)\left( {\sqrt a - 1} \right)}}.\left( {\sqrt a + 1} \right)\]

\[A = \frac{{ - 4}}{{\left( {\sqrt a + 1} \right)\left( {\sqrt a - 1} \right)}}.\left( {\sqrt a + 1} \right)\]

\[A = \frac{{ - 4}}{{\sqrt a - 1}}\]