a: \(A=\dfrac{x-9}{2\sqrt{x}+6}=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{2\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}-3}{2}\)
b: \(B=\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{3}{\sqrt{x}+3}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)-3\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x+3\sqrt{x}-3\sqrt{x}+9}{x-9}=\dfrac{x+9}{x-9}\)
c: \(C=\left(\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{3}{\sqrt{x}+3}\right)\cdot\left(\dfrac{x-9}{2\sqrt{x}+6}\right)\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)-3\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{2\sqrt{x}+6}\)
\(=\dfrac{x+3\sqrt{x}-3\sqrt{x}+9}{2\sqrt{x}+6}=\dfrac{x+9}{2\sqrt{x}+6}\)
