a: ĐKXĐ: x>=0; x<>1
\(P=\left(\frac{3x+\sqrt{9x}-3}{x+\sqrt{x}-2}+\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+2}\right):\frac{1}{x-1}\)
\(=\left(\frac{3x+3\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}+\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+2}\right)\cdot\left(x-1\right)\)
\(=\frac{3x+3\sqrt{x}-3+\sqrt{x}+2+\sqrt{x}-1}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}\cdot\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)\)
\(=\frac{3x+5\sqrt{x}-2}{\left(\sqrt{x}+2\right)}\left(\sqrt{x}+1\right)=\frac{\left(\sqrt{x}+2\right)\left(3\sqrt{x}-1\right)}{\left(\sqrt{x}+2\right)}\left(\sqrt{x}+1\right)\)
\(=\left(3\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
c: Khi \(x=4-2\sqrt3\) vào P, ta được:
\(P=\left(3\cdot\sqrt{4-2\sqrt3}-1\right)\left(\sqrt{4-2\sqrt3}+1\right)\)
\(=\left\lbrack3\left(\sqrt3-1\right)-1\right\rbrack\cdot\left\lbrack\sqrt3-1+1\right\rbrack=\left(3\sqrt3-4\right)\cdot\sqrt3=9-4\sqrt3\)
