P=(√x/√x-1-√x/1+√x):2x√x/1-x a,rút gọn P b,tính P khi x=√3

Đáp án:

$\begin{array}{l}
a)P = \left( {\dfrac{{\sqrt x }}{{\sqrt x  - 1}} - \dfrac{{\sqrt x }}{{1 + \sqrt x }}} \right):\dfrac{{2x\sqrt x }}{{1 - x}}\\
 = \dfrac{{\sqrt x \left( {1 + \sqrt x } \right) - \sqrt x \left( {\sqrt x  - 1} \right)}}{{\left( {\sqrt x  - 1} \right)\left( {1 + \sqrt x } \right)}}.\dfrac{{\left( {1 - \sqrt x } \right)\left( {1 + \sqrt x } \right)}}{{2x\sqrt x }}\\
 = \dfrac{{\sqrt x  + x - x + \sqrt x }}{{ - 1}}.\dfrac{1}{{2x\sqrt x }}\\
 = \dfrac{{ - 2\sqrt x }}{{2x\sqrt x }}\\
 =  - \dfrac{1}{x}\\
b)x = \sqrt 3 \left( {tmdk} \right)\\
P =  - \dfrac{1}{{\sqrt 3 }} =  - \dfrac{{\sqrt 3 }}{3}
\end{array}$