\(\left[\dfrac{3x+3\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}+\dfrac{1}{\sqrt{x}+2}-\dfrac{\sqrt{x}-2}{\sqrt{x}-1}\right]:\dfrac{\sqrt{x}}{\sqrt{x}+1}\left(x>0;x\ne1\right)\)
\(=\left[\dfrac{3x+3\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}-1}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}-\dfrac{x-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}\right].\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
\(=\dfrac{3x+3\sqrt{x}-3+\sqrt{x}-1-x+4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}.\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
\(=\dfrac{2x+4\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}.\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}.\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
\(=\dfrac{2\sqrt{x}+2}{\sqrt{x}-1}\)
