Упрощение алгебраических выражений. Задача 33

ОТВЕТ: -1.

\(\dfrac{{a-b}}{{a + b + 2\sqrt {ab} }}\,{\left( {\dfrac{{\sqrt {{a^{-1}}} -{b^{-\frac{1}{2}}}}}{{{a^{-\frac{1}{2}}} + {{\left( {\sqrt b } \right)}^{-1}}}}} \right)^{-1}} = \dfrac{{{{\left( {\sqrt a } \right)}^2}-{{\left( {\sqrt b } \right)}^2}}}{{{{\left( {\sqrt a } \right)}^2} + 2\sqrt a \sqrt b  + {{\left( {\sqrt b } \right)}^2}}} \cdot \dfrac{{\dfrac{1}{{\sqrt a }} + \dfrac{1}{{\sqrt b }}}}{{\dfrac{1}{{\sqrt a }}-\dfrac{1}{{\sqrt b }}}} = \)

\( = \dfrac{{\left( {\sqrt a -\sqrt b } \right)\left( {\sqrt a  + \sqrt b } \right)}}{{{{\left( {\sqrt a  + \sqrt b } \right)}^2}}} \cdot \dfrac{{\sqrt a  + \sqrt b }}{{\sqrt a  \cdot \sqrt b }} \cdot \dfrac{{\sqrt a  \cdot \sqrt b }}{{\sqrt b -\sqrt a }} = \dfrac{{-\left( {\sqrt b -\sqrt a } \right)}}{{\sqrt b -\sqrt a }} = -1.\)

Ответ:  \(-1.\)