a: \(A=\dfrac{\sqrt{x}-1}{x\left(x-1\right)}-\dfrac{\sqrt{x}+1+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
\(=\dfrac{1}{x\left(\sqrt{x}+1\right)}-\dfrac{2\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
\(=\dfrac{1-\sqrt{x}\left(2\sqrt{x}+1\right)}{x\left(\sqrt{x}+1\right)}=\dfrac{1-2x-\sqrt{x}}{x\left(\sqrt{x}+1\right)}\)
\(=\dfrac{-\left(2x+\sqrt{x}-1\right)}{x\left(\sqrt{x}+1\right)}=\dfrac{-\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{x\left(\sqrt{x}+1\right)}\)
\(=\dfrac{-2\sqrt{x}+1}{x}\)
b: khi \(x=4+2\sqrt{3}\) thì \(P=\dfrac{-2\left(\sqrt{3}+1\right)+1}{4+2\sqrt{3}}\)
\(=\dfrac{-2\sqrt{3}-2+1}{4+2\sqrt{3}}=\dfrac{-2\sqrt{3}-1}{4+2\sqrt{3}}\)
\(=\dfrac{\left(-2\sqrt{3}-1\right)\left(4-2\sqrt{3}\right)}{4}\)
\(=\dfrac{4-3\sqrt{3}}{2}\)
