M=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{1}{x-\sqrt{x}}\right):\left(\dfrac{1}{\sqrt{x}+1}+\dfrac{2}{x-1}\right)\)
=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}+\dfrac{2}{x-1}\right)\)
=\(\dfrac{\left(\sqrt{x}\cdot\sqrt{x}\right)-1}{\sqrt{x\left(\sqrt{x}-1\right)}}:\dfrac{\sqrt{x}-1+2}{x-1}\)
=\(\dfrac{x-1}{\sqrt{x}\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}+1}{x-1}\)
=\(\dfrac{x-1}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{x-1}{\sqrt{x+1}}\)
=\(\dfrac{\left(x-1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
=\(\dfrac{\left(x-1\right)^2}{\sqrt{x}\left(x-1\right)}\)
=\(\dfrac{x-1}{\sqrt{x}}=\dfrac{\sqrt{x}\left(x-1\right)}{x}\)
