$\begin{array}{l}
P = \dfrac{{2\sqrt 8 - \sqrt {12} }}{{\sqrt {18} - \sqrt {48} }} - \dfrac{{\sqrt 5 + \sqrt {27} }}{{\sqrt {30} + \sqrt {162} }}\\
P = \dfrac{{4\sqrt 2 - 2\sqrt 3 }}{{3\sqrt 2 - 4\sqrt 3 }} - \dfrac{{\sqrt 5 + \sqrt {27} }}{{\sqrt {30} + \sqrt {162} }}\\
P = \dfrac{{4\sqrt 2 - 2\sqrt 3 }}{{3\sqrt 2 - 4\sqrt 3 }} - \dfrac{{\sqrt 5 + \sqrt {27} }}{{\sqrt 6 \left( {\sqrt 5 + \sqrt {27} } \right)}}\\
P = \dfrac{{4\sqrt 2 - 2\sqrt 3 }}{{3\sqrt 2 - 4\sqrt 3 }} - \dfrac{1}{{\sqrt 6 }}\\
P = \dfrac{{\left( {4\sqrt 2 - 2\sqrt 3 } \right)\left( {3\sqrt 2 + 4\sqrt 3 } \right)}}{{ - 30}} - \dfrac{{\sqrt 6 }}{6}\\
P = \dfrac{{24 + 16\sqrt 6 - 6\sqrt 6 - 24}}{{ - 30}} - \dfrac{{\sqrt 6 }}{6}\\
P = \dfrac{{10\sqrt 6 }}{{ - 30}} - \dfrac{{\sqrt 6 }}{6} = \dfrac{{ - \sqrt 6 }}{3} - \dfrac{{\sqrt 6 }}{6} = \dfrac{{ - 3\sqrt 6 }}{6} = - \dfrac{{\sqrt 6 }}{2}\\
b)Q = \dfrac{{3 + 2\sqrt 3 }}{{\sqrt 3 }} + \dfrac{{2 + \sqrt 2 }}{{\sqrt 2 + 1}} - \left( {\sqrt 2 + \sqrt 3 } \right)\\
Q = \dfrac{{\sqrt 3 \left( {\sqrt 3 + 2} \right)}}{{\sqrt 3 }} + \dfrac{{\sqrt 2 \left( {\sqrt 2 + 1} \right)}}{{\sqrt 2 + 1}} - \sqrt 2 - \sqrt 3 \\
Q = \sqrt 3 + 2 + \sqrt 2 - \sqrt 2 - \sqrt 3 = 2
\end{array}$
