Rút gọn biểu thức \(A = \frac{{5 - 5\sqrt x }}{{x - 16}} - \frac{2}{{4 - \sqrt x }} + \frac{3}{{\sqrt x + 4}}\) (x ≥ 0, x ≠ 16).

Hướng dẫn giải

Với x ≥ 0, x ≠ 16, ta có:

\(A = \frac{{5 - 5\sqrt x }}{{x - 16}} - \frac{2}{{4 - \sqrt x }} + \frac{3}{{\sqrt x + 4}}\)

\(A = \frac{{5 - 5\sqrt x }}{{\left( {\sqrt x - 4} \right)\left( {\sqrt x + 4} \right)}} + \frac{{2\left( {\sqrt x + 4} \right)}}{{\left( {\sqrt x - 4} \right)\left( {\sqrt x + 4} \right)}} + \frac{{3\left( {\sqrt x - 4} \right)}}{{\left( {\sqrt x - 4} \right)\left( {\sqrt x + 4} \right)}}\)

\(A = \frac{{5 - 5\sqrt x + 2\sqrt x + 8 + 3\sqrt x - 12}}{{\left( {\sqrt x - 4} \right)\left( {\sqrt x + 4} \right)}}\)

\(A = \frac{1}{{\left( {\sqrt x - 4} \right)\left( {\sqrt x + 4} \right)}} = \frac{1}{{x - 16}}\).