$\begin{array}{l} B = \frac{x}{{\sqrt x - 1}} - \frac{{2x - \sqrt x }}{{x - \sqrt x }}\left( {x \ge 0;x \ne 1} \right)\\ = \frac{x}{{\sqrt x - 1}} - \frac{{\sqrt x \left( {2\sqrt x - 1} \right)}}{{\sqrt x \left( {\sqrt x - 1} \right)}}\\ = \frac{x}{{\sqrt x - 1}} - \frac{{2\sqrt x - 1}}{{\sqrt x - 1}}\\ = \frac{{x - 2\sqrt x + 1}}{{\sqrt x - 1}}\\ = \frac{{{{\left( {\sqrt x - 1} \right)}^2}}}{{\sqrt x - 1}}\\ = \sqrt x - 1 \end{array}$
