a: \(A=\dfrac{x-1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
b: \(B=\dfrac{a+2\sqrt{a}+1+a-2\sqrt{a}+1}{a-1}\cdot\dfrac{a-1}{4\left(a+1\right)}\)
\(=\dfrac{2\left(a+1\right)}{4\left(a+1\right)}=\dfrac{1}{2}\)
c: \(C=\left(\dfrac{x-1}{2\sqrt{x}}\right)^2\cdot\dfrac{x-2\sqrt{x}+1-x-2\sqrt{x}-1}{x-1}\)
\(=\dfrac{\left(x-1\right)^2}{4x}\cdot\dfrac{-4\sqrt{x}}{x-1}=\dfrac{-1}{\sqrt{x}}\cdot\dfrac{x-1}{1}=\dfrac{-x+1}{\sqrt{x}}\)
e: \(E=\dfrac{x-2\sqrt{x}+1-x-\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{-3\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{-3}{\sqrt{x}+1}\)
