\(A=\left(\dfrac{\sqrt{x}-3}{2-\sqrt{x}}+\dfrac{\sqrt{x}+2}{3+\sqrt{x}}-\dfrac{9-x}{x+\sqrt{x}-6}\right):\left(1-\dfrac{3\sqrt{x}-9}{x-9}\right)\)
\(=\left(\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\sqrt{x}+2}{\sqrt{x}+3}+\dfrac{x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\right):\left(1-\dfrac{3\left(\sqrt{x}-3\right)}{x-9}\right)\)
\(=\dfrac{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)+\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)+x-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}:\left(1-\dfrac{3}{\sqrt{x}+3}\right)\)
\(=\dfrac{9-x+x-4+x-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(=\dfrac{x-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}\cdot\dfrac{\sqrt{x}+3}{\sqrt{x}}=\dfrac{\sqrt{x}+2}{\sqrt{x}}\)