\(M=\left(1-\dfrac{4\sqrt{x}}{x-1}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{x-2\sqrt{x}}{x-1}\left(x>0;x\ne\left\{1;4\right\}\right)\\ =\left(1-\dfrac{4\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\dfrac{1}{\sqrt{x}-1}\right).\dfrac{x-1}{x-2\sqrt{x}}\\ =\dfrac{x-1-4\sqrt{x}+\sqrt{x}+1}{x-1}.\dfrac{x-1}{\sqrt{x}\left(\sqrt{x}-2\right)}\\ =\dfrac{x-3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\\ =\dfrac{\sqrt{x}-3}{\sqrt{x}-2}\)
\(M=\dfrac{1}{2}< =>\dfrac{\sqrt{x}-3}{\sqrt{x}-2}=\dfrac{1}{2}\\ < =>2\left(\sqrt{x}-3\right)=\sqrt{x}-2\\ < =>2\sqrt{x}-6=\sqrt{x}-2\\ < =>\sqrt{x}=4\\ < =>x=16\left(TMDK\right)\)
