Rút gọn biểu thức A=√a+3/√a−2−√a−1/√a+2+4√a−4/4−a với a≥0;a≠4

Với \[a \ge 0;a \ne 4\] ta có

\(A = \frac{{\sqrt a + 3}}{{\sqrt a - 2}} - \frac{{\sqrt a - 1}}{{\sqrt a + 2}} + \frac{{4\sqrt a - 4}}{{4 - a}}\)

\(A = \frac{{\left( {\sqrt a + 3} \right)\left( {\sqrt a + 2} \right)}}{{\left( {\sqrt a - 2} \right)\left( {\sqrt a + 2} \right)}} - \frac{{\left( {\sqrt a - 1} \right)\left( {\sqrt a - 2} \right)}}{{\left( {\sqrt a + 2} \right)\left( {\sqrt a - 2} \right)}} - \frac{{4\sqrt a - 4}}{{\left( {\sqrt a + 2} \right)\left( {\sqrt a - 2} \right)}}\)

\(A = \frac{{\left( {\sqrt a + 3} \right)\left( {\sqrt a + 2} \right) - \left( {\sqrt a - 1} \right)\left( {\sqrt a - 2} \right) - \left( {4\sqrt a - 4} \right)}}{{\left( {\sqrt a - 2} \right)\left( {\sqrt a + 2} \right)}}\)

\(A = \frac{{a + 2\sqrt a + 3\sqrt a + 6 - \left( {a - 2\sqrt a - \sqrt a + 2} \right) - \left( {4\sqrt a - 4} \right)}}{{\left( {\sqrt a - 2} \right)\left( {\sqrt a + 2} \right)}}\)

\(A = \frac{{a + 2\sqrt a + 3\sqrt a + 6 - a + 2\sqrt a + \sqrt a - 2 - 4\sqrt a + 4}}{{\left( {\sqrt a - 2} \right)\left( {\sqrt a + 2} \right)}}\)

\(A = \frac{{4\sqrt a + 8}}{{\left( {\sqrt a - 2} \right)\left( {\sqrt a + 2} \right)}}\)

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

\(A = \frac{4}{{\sqrt a - 2}}\)

Vậy \(A = \frac{4}{{\sqrt a - 2}}\) với \[a \ge 0;a \ne 4\].