Rút gọn biểu thức: \(B = \frac{{a + 2\sqrt a + 1}}{{\sqrt a + 1}} + \frac{{a - 1}}{{\sqrt a - 1}} - \sqrt a \).

ĐKXĐ: a ≥ 0; a ≠ 1.

\(B = \frac{{a + 2\sqrt a + 1}}{{\sqrt a + 1}} + \frac{{a - 1}}{{\sqrt a - 1}} - \sqrt a \)

\( = \frac{{{{\left( {\sqrt a + 1} \right)}^2}}}{{\sqrt a + 1}} + \frac{{\left( {\sqrt a - 1} \right)\left( {\sqrt a + 1} \right)}}{{\sqrt a - 1}} - \sqrt a \)

\( = \sqrt a + 1 + \sqrt a + 1 - \sqrt a \)\( = \sqrt a + 2\).