b: \(B=\left(\dfrac{\sqrt{x}+1}{x-4}-\dfrac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right)\cdot\dfrac{x\sqrt{x}+2x-4\sqrt{x}-8}{\sqrt{x}}\)
\(=\left(\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}-1}{\left(\sqrt{x}+2\right)^2}\right)\cdot\dfrac{\left(\sqrt{x}+2\right)\left(x-4\right)}{\sqrt{x}}\)
\(=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)^2}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)^2}{\sqrt{x}}\)
\(=\dfrac{x+3\sqrt{x}+2-x+3\sqrt{x}-2}{\sqrt{x}}=\dfrac{6\sqrt{x}}{\sqrt{x}}=6\)
c: \(C=\left(\dfrac{\sqrt{a}}{\sqrt{ab}-b}+\dfrac{2\sqrt{a}-\sqrt{b}}{\sqrt{ab}-a}\right):\left(\dfrac{1}{\sqrt{a}}+\dfrac{1}{\sqrt{b}}\right)\)
\(=\left(\dfrac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}-\dfrac{2\sqrt{a}-\sqrt{b}}{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}\right):\dfrac{\sqrt{a}+\sqrt{b}}{\sqrt{ab}}\)
\(=\dfrac{a-\sqrt{b}\left(2\sqrt{a}-\sqrt{b}\right)}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}\cdot\dfrac{\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\)
\(=\dfrac{a-2\sqrt{ab}+b}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}=\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
d: \(D=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{4\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2\sqrt{x}+1}{x\sqrt{x}-1}\right)\cdot\left(\sqrt{x}+\dfrac{2\sqrt{x}+1}{\sqrt{x}-1}\right)\)
\(=\left(\dfrac{\sqrt{x}\left(x+\sqrt{x}+1\right)-4\sqrt{x}\left(\sqrt{x}-1\right)-2\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\cdot\dfrac{x-\sqrt{x}+2\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\dfrac{x\sqrt{x}+x+\sqrt{x}-4x+4\sqrt{x}-2\sqrt{x}-1}{\left(\sqrt{x}-1\right)^2}\)
\(=\dfrac{x\sqrt{x}-3x+3\sqrt{x}-1}{\left(\sqrt{x}-1\right)^2}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)-3\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)^2}\)
\(=\dfrac{x-2\sqrt{x}+1}{\sqrt{x}-1}=\sqrt{x}-1\)
e: \(E=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}+4\sqrt{x}\right)\left(\sqrt{x}-\dfrac{1}{\sqrt{x}}\right)\)
\(=\dfrac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}-1\right)^2+4\sqrt{x}\left(x-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{x-1}{\sqrt{x}}\)
\(=\dfrac{x+2\sqrt{x}+1-x+2\sqrt{x}-1+4\sqrt{x}\left(x-1\right)}{\sqrt{x}}\)
\(=\dfrac{4\sqrt{x}\left(x-1+1\right)}{\sqrt{x}}=4x\)
