\(A=\left(\dfrac{x-3\sqrt{x}}{x-9}-1\right):\left(\dfrac{9-x}{x+\sqrt{x}-6}+\dfrac{\sqrt{x}-3}{\sqrt{x}-2}-\dfrac{\sqrt{x-2}}{\sqrt{x}+3}\right)\)
\(=\dfrac{x-3\sqrt{x}-x+9}{x-9}:\left[\dfrac{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}+\dfrac{\sqrt{x}-3}{\sqrt{x}-2}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\right]\)
\(=\dfrac{-3\left(\sqrt{x}-3\right)}{\left(\sqrt{x-3}\right)\left(\sqrt{x}+3\right)}:\left(\dfrac{3-\sqrt{x}+\sqrt{x}-3}{\sqrt{x}-2}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)
\(=\dfrac{-3}{\sqrt{x}+3}:\left(-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\right)=\dfrac{-3}{\sqrt{x}+3}.\left(-\dfrac{\sqrt{x}+3}{\sqrt{x}-2}\right)=\dfrac{3}{\sqrt{x}-2}\)
