a) \(M=\left(1-\dfrac{4\sqrt{x}}{x-1}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{x-2\sqrt{x}}{x-1}\)
\(M=\left[\dfrac{x-1}{x-1}-\dfrac{4\sqrt{x}}{x-1}+\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]:\dfrac{x-2\sqrt{x}}{x-1}\)
\(M=\dfrac{x-1-4\sqrt{x}+\sqrt{x}+1}{x-1}:\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{x-1}\)
\(M=\dfrac{x-3\sqrt{x}}{x-1}\cdot\dfrac{x-1}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(M=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{x-1}\cdot\dfrac{x-1}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(M=\dfrac{\sqrt{x}-3}{\sqrt{x}-2}\)
b) \(M=\dfrac{1}{2}\) khi:
\(\dfrac{\sqrt{x}-3}{\sqrt{x}-2}=\dfrac{1}{2}\)
\(\Leftrightarrow2\sqrt{x}-6=\sqrt{x}-2\)
\(\Leftrightarrow2\sqrt{x}-\sqrt{x}=-2+6\)
\(\Leftrightarrow\sqrt{x}=4\)
\(\Leftrightarrow x=16\left(tm\right)\)
