a: ĐKXĐ: \(\left\{{}\begin{matrix}x>1\\x\notin\left\{3;2\right\}\end{matrix}\right.\)
b: \(P=\left(\dfrac{1}{\sqrt{x}-\sqrt{x-1}}-\dfrac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\dfrac{2}{\sqrt{2}-\sqrt{x}}-\dfrac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
\(=\left(\dfrac{\sqrt{x}+\sqrt{x-1}}{x-x+1}-\dfrac{\left(\sqrt{x-1}-\sqrt{2}\right)\left(\sqrt{x-1}+\sqrt{2}\right)}{\sqrt{x-1}-\sqrt{2}}\right)\left(\dfrac{2\sqrt{x}-\sqrt{x}-\sqrt{2}}{\sqrt{x}\left(\sqrt{2}-\sqrt{x}\right)}\right)\)
\(=\left(\sqrt{x}+\sqrt{x-1}-\sqrt{x-1}-\sqrt{2}\right)\cdot\dfrac{\sqrt{x}-\sqrt{2}}{\sqrt{x}\left(\sqrt{x}-\sqrt{2}\right)}\cdot\left(-1\right)\)
\(=\dfrac{-\sqrt{x}+\sqrt{2}}{\sqrt{x}}\)
c: Khi \(x=3+2\sqrt{2}=\left(\sqrt{2}+1\right)^2\) thì
\(P=\dfrac{-\left(\sqrt{2}+1\right)+\sqrt{2}}{\sqrt{2}+1}=\dfrac{-1}{\sqrt{2}+1}=\dfrac{-\left(\sqrt{2}-1\right)}{1}=-\sqrt{2}+1\)
