a: \(A=\left(3+\dfrac{x+2\sqrt{x}}{\sqrt{x}+2}\right)\left(3+\dfrac{x-3\sqrt{x}}{3-\sqrt{x}}\right)\)
\(=\left(3+\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\right)\left(3-\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\sqrt{x}-3}\right)\)
\(=\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)=9-x\)
b: \(B=\left(1-\dfrac{3}{\sqrt{x}}\right)\left(\dfrac{1}{\sqrt{x}-3}+\dfrac{\sqrt{x}}{x+3\sqrt{x}}\right)\)
\(=\dfrac{\sqrt{x}-3}{\sqrt{x}}\left(\dfrac{1}{\sqrt{x}-3}+\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\)
\(=\dfrac{\sqrt{x}-3}{\sqrt{x}}\left(\dfrac{1}{\sqrt{x}-3}+\dfrac{1}{\sqrt{x}+3}\right)\)
\(=\dfrac{\sqrt{x}-3}{\sqrt{x}}\cdot\dfrac{\sqrt{x}+3+\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}=\dfrac{2}{\sqrt{x}+3}\)
c: \(C=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{x-\sqrt{x}}\right):\dfrac{\sqrt{x}+1}{x-1}\)
\(=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\dfrac{\sqrt{x}+1}{\left(\sqrt{x}+1\right)\cdot\left(\sqrt{x}-1\right)}\)
\(=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right)\cdot\left(\sqrt{x}-1\right)=\left(\sqrt{x}-1\right)\)
