\(V=\left(\dfrac{x-\sqrt{x}}{x-2\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{x+1}{\sqrt{x}-1}\left(x\ge0;x\ne1\right)\)
\(=\left[\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)^2}-\dfrac{1}{\sqrt{x}+1}\right]\cdot\dfrac{\sqrt{x}-1}{x+1}\)
\(=\left[\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}+1}\right]\cdot\dfrac{\sqrt{x}-1}{x+1}\)
\(=\left[\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]\cdot\dfrac{\sqrt{x}-1}{x+1}\)
\(=\dfrac{x+\sqrt{x}-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}-1}{x+1}\)
\(=\dfrac{x+1}{\left(\sqrt{x}+1\right)\left(x+1\right)}\)
\(=\dfrac{1}{\sqrt{x}+1}\)
#\(Toru\)
