\(P=\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)
\(=\frac{\sqrt{x}-\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}:\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\)\(\left(x>0,x\ne4,x\ne1\right)\)
\(=\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}:\frac{x-1-\left(x-4\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}:\frac{3}{\left(\sqrt{x}-2\right)\cdot\left(\sqrt{x}-1\right)}\)
\(=\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}{3}\)
\(=\frac{\sqrt{x}-2}{3\sqrt{x}}\)
ta có \(x=3-2\sqrt{2}\)
\(\Leftrightarrow x=2+1-2\sqrt{2}\)
\(\Leftrightarrow x=\left(\sqrt{2}-1\right)^2\)
thay x và biểu thức ta có :
\(\frac{\sqrt{\left(\sqrt{2}-1\right)^2}-2}{3\sqrt{\left(\sqrt{2}-1\right)^2}}\)
\(=\frac{\left|\sqrt{2}-1\right|-2}{3\left|\sqrt{2}-1\right|}\)
\(=\frac{\sqrt{2}-1-2}{3\left(\sqrt{2}-1\right)}\)
\(=\frac{\left(\sqrt{2}-3\right)\left(\sqrt{2}+1\right)}{3\left(2-1\right)}\)
\(=\frac{2+\sqrt{2}-3\sqrt{2}-3}{3}\)
\(=\frac{-1-2\sqrt{2}}{3}\)
\(=-\frac{1+2\sqrt{2}}{3}\)
có sai cho mình xin lỗi nha !
