\(\dfrac{\sqrt{x}+3}{\sqrt{x}+2}+\dfrac{2}{\sqrt{x}-3}-\dfrac{2\sqrt{x}-1}{x-\sqrt{x}-6}.\) \(\left(x\ge0;x\ne9\right).\)
\(=\dfrac{\sqrt{x}+3}{\sqrt{x}+2}+\dfrac{2}{\sqrt{x}-3}-\dfrac{2\sqrt{x}-1}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}.\)
\(=\dfrac{x-9+2\sqrt{x}+4-2\sqrt{x}+1}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\dfrac{x-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}.\)
\(=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}-2}{\sqrt{x}-3}.\)
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