Question

Rút gọn biểu thức: \(\dfrac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\dfrac{2b}{a-b}\) với a ≥ 0, b ≥ 0, a ≠ b.

Answer 1

\(\begin{array}{l}\frac{{\sqrt a }}{{\sqrt a  - \sqrt b }} - \frac{{\sqrt b }}{{\sqrt a  + \sqrt b }} - \frac{{2b}}{{a - b}}\\ = \frac{{\sqrt a \left( {\sqrt a  + \sqrt b } \right)}}{{\left( {\sqrt a  - \sqrt b } \right)\left( {\sqrt a  + \sqrt b } \right)}} - \frac{{\sqrt b \left( {\sqrt a  - \sqrt b } \right)}}{{\left( {\sqrt a  + \sqrt b } \right)\left( {\sqrt a  - \sqrt b } \right)}} - \frac{{2b}}{{a - b}}\\ = \frac{{a + \sqrt {ab} }}{{a - b}} - \frac{{\sqrt {ab}  - b}}{{a - b}} - \frac{{2b}}{{a - b}}\\ = \frac{{a + \sqrt {ab}  - \sqrt {ab}  + b - 2b}}{{a - b}}\\ = \frac{{a - b}}{{a - b}}= 1.\end{array}\)