1: \(P=\dfrac{3\left(x+2\sqrt{x}\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
\(=\dfrac{3\left(x+2\sqrt{x}\right)-\left(\sqrt{x}+2\right)^2-\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{3x+6\sqrt{x}-x-4\sqrt{x}-4-x+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x+2\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}+3}{\sqrt{x}+2}\)
2: \(x=6-2\sqrt{5}=\left(\sqrt{5}-1\right)^2\)
Thay \(x=\left(\sqrt{5}-1\right)^2\) vào P, ta được:
\(P=\dfrac{\sqrt{5}-1+3}{\sqrt{5}-1+2}=\dfrac{\sqrt{5}+2}{\sqrt{5}+1}=\dfrac{3+\sqrt{5}}{4}\)
