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\(a,M=\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
\(=\left(\frac{2x-2\sqrt{2}x+2\sqrt{2x}-1}{2x-1}-1\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x+1}}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
\(=\left(\frac{-2\sqrt{2}x+2\sqrt{2x}}{2x-1}\right):\left(1+\frac{x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1-\left(2x+\sqrt{2x}+x\sqrt{2}+\sqrt{x}\right)}{2x-1}\right)\)
\(=\left(\frac{-2\sqrt{2}x+2\sqrt{2x}}{2x-1}\right):\left(\frac{-2\sqrt{x}-2}{2x-1}\right)\)
\(=\frac{-\sqrt{2}x+\sqrt{2x}}{\sqrt{x}-1}\)
\(=\frac{-\sqrt{2x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)
\(=-\sqrt{2x}\)
\(b,x=\frac{1}{2}\left(3+2\sqrt{2}\right)\)
\(x=\frac{1}{2}\left(1+2\sqrt{2}+2\right)\)
\(x=\frac{1}{2}\left(1+\sqrt{2}\right)^2\)
Thay \(x=\frac{1}{2}\left(1+\sqrt{2}\right)^2\) vào \(M=-\sqrt{2x}\) ta được:
\(M=-\sqrt{2.\frac{1}{2}\left(1+\sqrt{2}\right)^2}\)
\(M=-1-\sqrt{2}\)
Vậy ..............