a) \(M=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{x-1}\right):\left(\dfrac{2}{x}-\dfrac{2-x}{x\sqrt{x}+x}\right)\left(đk:x>0,x\ne1\right)\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\dfrac{2\left(\sqrt{x}+1\right)-2+x}{x\left(\sqrt{x}+1\right)}=\dfrac{x+2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{x\left(\sqrt{x}+1\right)}{x+2\sqrt{x}}=\dfrac{x}{\sqrt{x}-1}\)
b) \(M=\dfrac{x}{\sqrt{x}-1}=-\dfrac{1}{2}\)
\(\Leftrightarrow2x+\sqrt{x}-1=0\Leftrightarrow\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)=0\)
\(\Leftrightarrow\sqrt{x}=\dfrac{1}{2}\Leftrightarrow x=\dfrac{1}{4}\left(tm\right)\)( do \(\sqrt{x}+1\ge1>0\))