\(B=\left(\dfrac{\sqrt{x}-4}{x-2\sqrt{x}}+\dfrac{3}{\sqrt{x}-2}\right):\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}}\right)\left(x>0;x\ne4\right)\\ B=\dfrac{\sqrt{x}-4+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}:\dfrac{x-x+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\\ B=\dfrac{4\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{4}=\sqrt{x}-1\)
Thay \(x=3+\sqrt{8}=3+2\sqrt{2}=\left(\sqrt{2}+1\right)^2\) vào B:
\(B=\sqrt{\left(\sqrt{2}+1\right)^2}-1=\sqrt{2}+1-1=\sqrt{2}\)
Ta có: \(B=\left(\dfrac{\sqrt{x}-4}{x-2\sqrt{x}}+\dfrac{3}{\sqrt{x}-2}\right):\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}}\right)\)
\(=\dfrac{\sqrt{x}-4+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}:\dfrac{x-x+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{4\sqrt{x}-4}{4}\)
\(=\sqrt{x}-1\)
Thay \(x=3+2\sqrt{2}\) vào B, ta được:
\(B=\sqrt{2}+1-1=\sqrt{2}\)
