a: \(M=\left(\frac{3}{1-\sqrt{x}}+\frac{1}{1+\sqrt{x}}\right)\cdot\frac{1+\sqrt{x}}{2+\sqrt{x}}\)
\(=\frac{3\left(1+\sqrt{x}\right)+1-\sqrt{x}}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}\cdot\frac{1+\sqrt{x}}{2+\sqrt{x}}=\frac{2\sqrt{x}+4}{1-\sqrt{x}}\cdot\frac{1}{2+\sqrt{x}}=\frac{2}{1-\sqrt{x}}\)
b: M>2
=>M-2>0
=>\(\frac{2}{1-\sqrt{x}}-2>0\)
=>\(\frac{2-2\left(1-\sqrt{x}\right)}{1-\sqrt{x}}>0\)
=>\(\frac{2\sqrt{x}}{1-\sqrt{x}}>0\)
=>\(1-\sqrt{x}>0\)
=>\(\sqrt{x}<1\)
=>0<x<1
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