\(B=\left(\dfrac{y+2}{y\sqrt{y}-1}+\dfrac{\sqrt{y}}{y+\sqrt{y}-1}+\dfrac{1}{1-\sqrt{y}}\right):\dfrac{\sqrt{y}-1}{2}\)
\(=\left[\dfrac{y+2}{\left(\sqrt{y}-1\right)\left(y+\sqrt{y}+1\right)}+\dfrac{\sqrt{y}\left(\sqrt{y}-1\right)}{\left(\sqrt{y}-1\right)\left(y+\sqrt{y}+1\right)}-\dfrac{y+\sqrt{y}+1}{\left(\sqrt{y}-1\right)\left(y+\sqrt{y}+1\right)}\right]:\dfrac{\sqrt{y}-1}{2}\)
\(=\left[\dfrac{y+2+y-\sqrt{y}-y-\sqrt{y}-1}{\left(\sqrt{y}-1\right)\left(y+\sqrt{y}+1\right)}\right].\dfrac{2}{\sqrt{y}-1}\)
\(=\dfrac{y-2\sqrt{y}+1}{\left(\sqrt{y}-1\right)\left(y+\sqrt{y}+1\right)}.\dfrac{2}{\sqrt{y}-1}=\dfrac{2}{y+\sqrt{y}+1}\)