1. $P= \dfrac{(\sqrt{x}+1)(\sqrt{2x}-1)+(\sqrt{2x}+1)(\sqrt{2x}+\sqrt{x})-(\sqrt{2x}+1)(\sqrt{2x}-1)}{(\sqrt{2x}+1)(\sqrt{2x}-1)} : \dfrac{(\sqrt{2x}+1)(\sqrt{2x}-1)+(\sqrt{x}+1)(\sqrt{2x}-1)-(\sqrt{2x}-\sqrt{x})(\sqrt{2x}+1)}{(\sqrt{2x}+1)(\sqrt{2x}-1)}$
$=\dfrac{\sqrt{2}x-\sqrt{x}+\sqrt{2x}-1+2x-\sqrt{2}x+\sqrt{2x}-\sqrt{x}-(2x-1)}{2x-1}:\dfrac{2x-1+\sqrt{2}x-\sqrt{x}+\sqrt{2x}-1-(2x+\sqrt{2x}+\sqrt{2}x+\sqrt{x})}{2x-1}$
$=\dfrac{2\sqrt{x}(\sqrt{2}-1)}{2x-1}:\dfrac{-2(\sqrt{x}+1)}{2x-1}=\dfrac{2\sqrt{x}(\sqrt{2}-1)}{-2(\sqrt{x}+1)}$
2. Với $x=\dfrac{3+2\sqrt{2}}{2}=\dfrac{(\sqrt{2}+1)^{2}}{2}\Rightarrow \sqrt{x}=\dfrac{\sqrt{2}+1}{\sqrt{2}}$ thì:
$P=\dfrac{2.\dfrac{\sqrt{2}+1}{\sqrt{2}}.(\sqrt{2}-1)}{-2\left( \dfrac{\sqrt{2}+1}{\sqrt{2}}+1\right)}$
$=\dfrac{2.\dfrac{2-1}{\sqrt{2}}}{-2.\dfrac{ \sqrt{2}+1+\sqrt{2}}{\sqrt{2}}}=\dfrac{1}{-(2\sqrt{2}+1)}$