Đáp án:
\(\begin{array}{l}
G = \sqrt a - \sqrt b \\
H = \dfrac{{\sqrt {xy} }}{{\sqrt x + \sqrt y }}\\
K = \dfrac{{\sqrt x + 2}}{{\sqrt x - 3}}\\
M = \dfrac{{\sqrt x - 4}}{{\sqrt x + 1}}\\
N = \dfrac{{2\left( {a + b} \right)}}{{a - b}}\\
P = \dfrac{{\sqrt {ab} }}{{\sqrt a + \sqrt b }}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
G = \dfrac{{\left( {\sqrt a - \sqrt b } \right)\left( {a + \sqrt {ab} + b} \right)}}{{a + \sqrt {ab} + b}}\\
= \sqrt a - \sqrt b \\
H = \dfrac{{\sqrt {xy} \left( {\sqrt x - \sqrt y } \right)}}{{\left( {\sqrt x - \sqrt y } \right)\left( {\sqrt x + \sqrt y } \right)}}\\
= \dfrac{{\sqrt {xy} }}{{\sqrt x + \sqrt y }}\\
K = \dfrac{{\left( {\sqrt x + 2} \right)\left( {\sqrt x + 3} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\\
= \dfrac{{\sqrt x + 2}}{{\sqrt x - 3}}\\
M = \dfrac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x - 4} \right)}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \dfrac{{\sqrt x - 4}}{{\sqrt x + 1}}\\
N = \dfrac{{a + 2\sqrt {ab} + b + a - 2\sqrt {ab} + b}}{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)}}\\
= \dfrac{{2\left( {a + b} \right)}}{{a - b}}\\
P = \dfrac{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)}}{{\sqrt a - \sqrt b }} - \dfrac{{\left( {\sqrt a - \sqrt b } \right)\left( {a + \sqrt {ab} + b} \right)}}{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)}}\\
= \sqrt a + \sqrt b - \dfrac{{a + \sqrt {ab} + b}}{{\sqrt a + \sqrt b }}\\
= \dfrac{{a + 2\sqrt {ab} + b - a - \sqrt {ab} - b}}{{\sqrt a + \sqrt b }}\\
= \dfrac{{\sqrt {ab} }}{{\sqrt a + \sqrt b }}
\end{array}\)
