\(\left(\dfrac{3\sqrt{x}+6}{x-4}+\dfrac{\sqrt{x}}{\sqrt{x}-2}\right):\dfrac{x-9}{\sqrt{x}-3}\left(dkxd:x\ne9,x\ne4,x\ge0\right)\)
\(=\left(\dfrac{3\sqrt{x}+6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}}{\sqrt{x}-2}\right):\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{\sqrt{x}-3}\)
\(=\left(\dfrac{3\sqrt{x}+6+\sqrt{x}\left(\sqrt{x}+2\right)}{(\sqrt{x}-2)\left(\sqrt{x}+2\right)}\right).\dfrac{1}{\sqrt{x}+3}\)
\(=\dfrac{3\sqrt{x}+6+x+2\sqrt{x}}{x-4}.\dfrac{1}{\sqrt{x}+3}\)
\(=\dfrac{x+5\sqrt{x}+6}{x-4}.\dfrac{1}{\sqrt{x}+3}\)
\(=\dfrac{x+2\sqrt{x}+3\sqrt{x}+6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{1}{\sqrt{x}+3}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)+3\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{1}{\sqrt{x}+3}\)
\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{1}{\sqrt{x}+3}\)
\(=\dfrac{1}{\sqrt{x}-2}\)
