\(ĐKXĐ:\left\{{}\begin{matrix}x\ge0\\x\ne1\end{matrix}\right.\)
\(B=A\left(x-1\right)\)
\(=\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{2}{\sqrt{x}+1}-\frac{2}{x-1}\right)\left(x-1\right)\)
\(=\sqrt{x}\left(\sqrt{x}+1\right)-2\left(\sqrt{x}-1\right)-2\)
\(=x+\sqrt{x}-2\sqrt{x}+2-2\)
\(=x-\sqrt{x}\)
\(=x-2.\frac{1}{2}\sqrt{x}+\frac{1}{4}-\frac{1}{4}\)
\(=\left(\sqrt{x}-\frac{1}{2}\right)^2-\frac{1}{4}\)
\(\ge-\frac{1}{4}\)
Dấu "=" xảy ra khi \(\sqrt{x}-\frac{1}{2}=0\Leftrightarrow\sqrt{x}=\frac{1}{2}\Leftrightarrow x=\frac{1}{4}\left(tm\right)\)
Vậy \(Min_B=-\frac{1}{4}\) khi \(x=\frac{1}{4}\)
