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\((\frac{3x+3\sqrt{x}-3}{x+\sqrt{x}-2}+\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+2}-2):\frac{1}{x-1}\)
=\(\left(\frac{3x+3\sqrt{x}-3}{(\sqrt{x}+2)\left(\sqrt{x}-1\right)}+\frac{\sqrt{x}+2}{(\sqrt{x}+2)\left(\sqrt{x}-1\right)}+\frac{\sqrt{x}-1}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}-\frac{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\left(\frac{3x+3\sqrt{x}-3+\sqrt{x}+2+\sqrt{x}-1-\left(2\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\left(\frac{3x+5\sqrt{x}-2-\left(2x+4\sqrt{x}-2\sqrt{x}-4\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\left(\frac{3x+5\sqrt{x}-2-2x-2\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right).\left(x-1\right)\)
=\(\frac{x+3\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}.\left(x-1\right)\)
=\(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}.\left(x-1\right)\)
=\(\frac{\left(\sqrt{x}+1\right)\left(x-1\right)}{\left(\sqrt{x}-1\right)}\)=\(\left(\sqrt{x}+1\right)^2\)
\(\left(\dfrac{3x-3\sqrt{x}-3}{x+\sqrt{x}-2}+\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}+2}\right)\) : \(\dfrac{1}{\sqrt{x}+2}\)
=\(\dfrac{3x-3\sqrt{x}-3+\sqrt{x}+2-\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+2)}\) .\(\sqrt{x}+2\)
=\(\dfrac{(3x-3\sqrt{x})(\sqrt{x}+2)}{(\sqrt{x}-1)(\sqrt{x}+2)}\)
=\(\dfrac{3\sqrt{x}(\sqrt{x}-1)(\sqrt{x}+2)}{(\sqrt{x}-1)(\sqrt{x}+2)}\) =\(3\sqrt{x}\)
\(\frac{1}{1-x^2}+1=\frac{3x}{\sqrt{1-x^2}}\)
\(\Leftrightarrow1.\sqrt{-x^2+1}+1.\left(-x^2+1\right).\sqrt{-x^2+1}=3x.\left(-x^2+1\right)\)
\(\Leftrightarrow\sqrt{-x^2+1}+\sqrt{-x^2+1}.\left(-x^2+1\right)=3\left(-x^2+1\right)\)
\(\Leftrightarrow-\sqrt{-x^2+1}.x^2+2\sqrt{-x^2+1}=-3x^2+3x\)
\(\Leftrightarrow\sqrt{-x^2+1}.\left(x^2+2\right)=-3x^3+3x\)
\(\Leftrightarrow\sqrt{-x^2+1}=-\frac{3x^2}{-x^2+2}+\frac{3x}{-x^2+2}\)
\(\Leftrightarrow\sqrt{-x^2+1}=\frac{-3x^2+3x}{-x^2+2}\)
\(\Leftrightarrow\left(\sqrt{-x^2+1}\right)^2=\left(\frac{-3x^2+3x}{-x^2+2}\right)^2\)
\(\Leftrightarrow-x^2+1=\frac{9x^6-18x^4+9x^2}{x^4-4x^2+4}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{\frac{1}{2}}\\x=\frac{2\sqrt{5}}{5}\end{cases}}\)
Vậy nghiệm phương trình là \(\left\{\sqrt{\frac{1}{2}};\frac{2\sqrt{5}}{5}\right\}\)