Giải thích các bước giải: 
 1)
 \[\begin{array}{l}
 a,\\
 \sqrt {18}  - 2\sqrt {50}  + 3\sqrt 8  = \sqrt {{{2.3}^2}}  - 2\sqrt {{{2.5}^2}}  + 3\sqrt {{{2.2}^2}}  = 3\sqrt 2  - 10\sqrt 2  + 6\sqrt 2  =  - \sqrt 2 \\
 b,\\
 {\left( {\sqrt 7  - \sqrt 3 } \right)^2} + \sqrt {84}  = 7 - 2\sqrt {21}  + 3 + \sqrt {{{21.2}^2}}  = 10\\
 c,\\
 \left( {\frac{{6 - 2\sqrt 2 }}{{3 - \sqrt 2 }} - \frac{5}{{\sqrt 5 }}} \right):\frac{1}{{2 - \sqrt 5 }} = \left( {2 - \sqrt 5 } \right).\left( {2 - \sqrt 5 } \right) = {\left( {2 - \sqrt 5 } \right)^2} = 4 - 4\sqrt 5  + 5 = 9 - 4\sqrt 5 
 \end{array}\]
 2,
 \[\begin{array}{l}
 a,\\
 \sqrt {{{\left( {2x + 3} \right)}^2}}  = 4 \Leftrightarrow \left[ \begin{array}{l}
 2x + 3 = 4\left( {x \ge \frac{{ - 3}}{2}} \right)\\
 2x + 3 =  - 4\left( {x < \frac{{ - 3}}{2}} \right)
 \end{array} \right.\\
 b,\\
 \sqrt {9x}  - 5\sqrt x  = 6 - 4\sqrt x \\
  \Leftrightarrow 3\sqrt x  - 5\sqrt x  = 6 - 4\sqrt x \\
  \Leftrightarrow 2\sqrt x  = 6\\
  \Leftrightarrow x = 9
 \end{array}\]
 3)
 \[\begin{array}{l}
 a,\\
 Q = \left( {\frac{1}{{\sqrt a  + 1}} - \frac{1}{{a + \sqrt a }}} \right):\frac{{\sqrt a  - 1}}{{a + 2\sqrt a  + 1}}\\
 DK{\rm{XD: a > 0}}\\
  \Leftrightarrow {\rm{Q = }}\left( {\frac{1}{{\sqrt a  + 1}} - \frac{1}{{\sqrt a \left( {\sqrt a  + 1} \right)}}} \right):\frac{{\sqrt a  - 1}}{{{{\left( {\sqrt a  + 1} \right)}^2}}}\\
  \Leftrightarrow Q = \left( {\frac{{\sqrt a  - 1}}{{\sqrt a \left( {\sqrt a  + 1} \right)}}} \right).\frac{{{{\left( {\sqrt a  + 1} \right)}^2}}}{{\sqrt a  - 1}}\left( {a \ne 1} \right)\\
  \Leftrightarrow Q = \frac{{\sqrt a  + 1}}{{\sqrt a }} = 1 + \frac{1}{{\sqrt a }}\\
 b,\\
 Q > 2 \Leftrightarrow \frac{1}{{\sqrt a }} > 1 \Leftrightarrow a < 1
 \end{array}\]