Đáp án:
\(\begin{array}{l}
7A)\\
a)M = \dfrac{{\sqrt {xy} }}{{\sqrt x + \sqrt y }}\\
b)N = \dfrac{{1 - \sqrt a }}{{2\sqrt a - 1}}\\
7B)\\
a)Q = \dfrac{{\sqrt {xy} }}{{\sqrt x - \sqrt y }}\\
b)P = 0
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
7A)\\
a)M = \dfrac{{\sqrt {xy} \left( {\sqrt x + \sqrt y } \right)}}{{{{\left( {\sqrt x + \sqrt y } \right)}^2}}}\\
= \dfrac{{\sqrt {xy} }}{{\sqrt x + \sqrt y }}\\
b)N = \dfrac{{ - 2a + 3\sqrt a - 1}}{{{{\left( {2\sqrt a - 1} \right)}^2}}}\\
= \dfrac{{\left( {1 - \sqrt a } \right)\left( {2\sqrt a - 1} \right)}}{{{{\left( {2\sqrt a - 1} \right)}^2}}}\\
= \dfrac{{1 - \sqrt a }}{{2\sqrt a - 1}}\\
7B)\\
a)Q = \dfrac{{\sqrt {xy} \left( {\sqrt x - \sqrt y } \right)}}{{{{\left( {\sqrt x - \sqrt y } \right)}^2}}}\\
= \dfrac{{\sqrt {xy} }}{{\sqrt x - \sqrt y }}\\
b)P = \dfrac{{{{\left( {\sqrt a + 2} \right)}^2}}}{{\sqrt a + 2}} - \dfrac{{\left( {\sqrt a + 2} \right)\left( {\sqrt a - 2} \right)}}{{\sqrt a - 2}}\\
= \sqrt a + 2 - \left( {\sqrt a + 2} \right)\\
= 0
\end{array}\)
