\((\frac{3x+3\sqrt{x}-3}{x+\sqrt{x}-2}+\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+2}-2):\frac{1}{x-1}\)
=\(\left(\frac{3x+3\sqrt{x}-3}{(\sqrt{x}+2)\left(\sqrt{x}-1\right)}+\frac{\sqrt{x}+2}{(\sqrt{x}+2)\left(\sqrt{x}-1\right)}+\frac{\sqrt{x}-1}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}-\frac{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\left(\frac{3x+3\sqrt{x}-3+\sqrt{x}+2+\sqrt{x}-1-\left(2\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\left(\frac{3x+5\sqrt{x}-2-\left(2x+4\sqrt{x}-2\sqrt{x}-4\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\left(\frac{3x+5\sqrt{x}-2-2x-2\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\frac{x+3\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}.\left(x-1\right)\)
=\(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}.\left(x-1\right)\)
=\(\frac{\left(\sqrt{x}+1\right)\left(x-1\right)}{\left(\sqrt{x}-1\right)}\)=\(\left(\sqrt{x}+1\right)^2\)
