a: Thay \(x=7+4\sqrt3=\left(2+\sqrt3\right)^2\) vào A, ta được:
\(A=\frac{\sqrt{\left(2+\sqrt3\right)^2}-1}{\sqrt{\left(2+\sqrt3\right)^2}-2}=\frac{2+\sqrt3-1}{2+\sqrt3-2}=\frac{\sqrt3+1}{\sqrt3}=\frac{3+\sqrt3}{3}\)
b: \(B=\frac{-\sqrt{x}+2}{x-\sqrt{x}-2}-\frac{x}{x-2\sqrt{x}}\)
\(=\frac{-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}-\frac{x}{\sqrt{x}\left(\sqrt{x}-2\right)}=\frac{-1}{\sqrt{x}+1}-\frac{\sqrt{x}}{\sqrt{x}-2}\)
\(=\frac{-\sqrt{x}+2-\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}=\frac{-\sqrt{x}+2-x-\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}=\frac{-x-2\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
P=B:A
\(=\frac{-x-2\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\cdot\frac{\sqrt{x}-2}{\sqrt{x}-1}=\frac{-x-2\sqrt{x}+2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
