Giải thích các bước giải:
\(\begin{array}{l}
10,\\
P = \left( {\dfrac{{4\sqrt x }}{{2 + \sqrt x }} + \dfrac{{8x}}{{4 - x}}} \right):\left( {\dfrac{{\sqrt x - 1}}{{x - 2\sqrt x }} - \dfrac{2}{{\sqrt x }}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( \begin{array}{l}
x > 0\\
x \ne 4
\end{array} \right)\\
= \left( {\dfrac{{4\sqrt x }}{{2 + \sqrt x }} + \dfrac{{8x}}{{\left( {2 - \sqrt x } \right)\left( {2 + \sqrt x } \right)}}} \right):\left( {\dfrac{{\sqrt x - 1}}{{\sqrt x \left( {\sqrt x - 2} \right)}} - \dfrac{2}{{\sqrt x }}} \right)\\
= \dfrac{{4\sqrt x .\left( {2 - \sqrt x } \right) + 8x}}{{\left( {2 - \sqrt x } \right)\left( {2 + \sqrt x } \right)}}:\dfrac{{\left( {\sqrt x - 1} \right) - 2.\left( {\sqrt x - 2} \right)}}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{8\sqrt x - 4x + 8x}}{{\left( {2 - \sqrt x } \right)\left( {2 + \sqrt x } \right)}}:\dfrac{{\sqrt x - 1 - 2\sqrt x + 4}}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{4x + 8\sqrt x }}{{\left( {2 - \sqrt x } \right)\left( {2 + \sqrt x } \right)}}:\dfrac{{3 - \sqrt x }}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{4\sqrt x \left( {\sqrt x + 2} \right)}}{{\left( {2 - \sqrt x } \right)\left( {2 + \sqrt x } \right)}}.\dfrac{{\sqrt x \left( {\sqrt x - 2} \right)}}{{3 - \sqrt x }}\\
= \dfrac{{4{x^2}}}{{\sqrt x - 3}}\\
9,\\
P = \left( {\dfrac{1}{{\sqrt x - \sqrt {x - 1} }} - \dfrac{{x - 3}}{{\sqrt {x - 1} - \sqrt 2 }}} \right)\left( {\dfrac{2}{{\sqrt 2 - \sqrt x }} - \dfrac{{\sqrt x + \sqrt 2 }}{{\sqrt {2x} - x}}} \right)\,\,\,\,\,\,\,\,\,\,\left( \begin{array}{l}
x > 0\\
x \ne 2
\end{array} \right)\\
= \left( {\dfrac{{\sqrt x + \sqrt {x - 1} }}{{\left( {\sqrt x - \sqrt {x - 1} } \right)\left( {\sqrt x + \sqrt {x - 1} } \right)}} - \dfrac{{\left( {x - 3} \right)\left( {\sqrt {x - 1} + \sqrt 2 } \right)}}{{\left( {\sqrt {x - 1} - \sqrt 2 } \right)\left( {\sqrt {x - 1} + \sqrt 2 } \right)}}} \right).\left( {\dfrac{2}{{\sqrt 2 - \sqrt x }} - \dfrac{{\sqrt x + \sqrt 2 }}{{\sqrt x .\left( {\sqrt 2 - \sqrt x } \right)}}} \right)\\
= \left( {\dfrac{{\sqrt x + \sqrt {x - 1} }}{{x - \left( {x - 1} \right)}} - \dfrac{{\left( {x - 3} \right)\left( {\sqrt {x - 1} + \sqrt 2 } \right)}}{{\left( {x - 1} \right) - 2}}} \right).\dfrac{{2\sqrt x - \left( {\sqrt x + \sqrt 2 } \right)}}{{\sqrt x .\left( {\sqrt 2 - \sqrt x } \right)}}\\
= \left[ {\left( {\sqrt x + \sqrt {x - 1} } \right) - \left( {\sqrt {x - 1} + \sqrt 2 } \right)} \right].\dfrac{{\sqrt x - \sqrt 2 }}{{\sqrt x .\left( {\sqrt 2 - \sqrt x } \right)}}\\
= \left( {\sqrt x - \sqrt 2 } \right).\dfrac{{ - 1}}{{\sqrt x }}\\
= \dfrac{{\sqrt 2 - \sqrt x }}{{\sqrt x }}
\end{array}\)
