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