$a)ĐKXĐ: x\ge0; x\ne1$
$P=(\dfrac{2}{\sqrt{x}-1}+\dfrac{x}{\sqrt{x}+1}).\dfrac{\sqrt{x}}{x+\sqrt{x}+2}$
$P=\dfrac{2(\sqrt{x}+1)+\sqrt{x}(\sqrt{x}-1)}{(\sqrt{x}+1)(\sqrt{x}-1)}.\dfrac{\sqrt{x}}{x+\sqrt{x}+2}$
$P=\dfrac{2\sqrt{x}+2+x-\sqrt{x}}{(\sqrt{x}+1)(\sqrt{x}-1)}.\dfrac{\sqrt{x}}{x+\sqrt{x}+2}$
$P=\dfrac{x+2\sqrt{x}+2}{(\sqrt{x}+1)(\sqrt{x}-1)}.\dfrac{\sqrt{x}}{x+\sqrt{x}+2}$
$P=\dfrac{\sqrt{x}}{(\sqrt{x}+1)(\sqrt{x}-1)}$
$P=\dfrac{\sqrt{x}}{x-1}$
Vậy với $x\ge0; x\ne1$ thì $P=\dfrac{\sqrt{x}}{x-1}$
$b)$Thay $x=3+2\sqrt{2}(t/m)$ vào $P$ ta được:
$P=\dfrac{\sqrt{3+2\sqrt{2}}}{3+2\sqrt{2}-1}$
$P=\dfrac{\sqrt{2+2\sqrt{2}+1}}{2+2\sqrt{2}}$
$P=\dfrac{\sqrt{(\sqrt{2}+1)^2}}{2(1+\sqrt{2})}$
$P=\dfrac{\sqrt{2}+1}{2(1+\sqrt{2})}$
$P=\dfrac{1}{2}$
Vậy với $x=3+2\sqrt{2}$ thì $P=\dfrac{1}{2}$
