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