$\displaystyle \begin{array}{{>{\displaystyle}l}} P=\left(\frac{1}{\sqrt{x} -1} -\frac{2}{x\sqrt{x} -x+\sqrt{x} -1}\right) :\left( 1-\frac{\sqrt{x}}{x+1}\right) \ với\ x\leqslant 0;x\#1\\ a) \ P=\left(\frac{1}{\sqrt{x} -1} -\frac{2}{x\left(\sqrt{x} -1\right) +\sqrt{x} -1}\right) :\frac{x+1-\sqrt{x}}{x+1}\\ P=\frac{x+1-2}{( x+1)\left(\sqrt{x} -1\right)} .\frac{x+1}{x+1-\sqrt{x}}\\ P=\frac{( x-1)( x+1)}{( x+1)\left(\sqrt{x} -1\right)\left( x+1-\sqrt{x}\right)} =\frac{\sqrt{x} +1}{x-\sqrt{x} +1}\\ b) \ Ta\ có\ :\ \sqrt{x} +1 >0\ với\ mọi\ x\ \\ x-\sqrt{x} +1=x-\frac{1}{2} 2\sqrt{x} +\frac{1}{4} +\frac{3}{4}\\ =\left( x-\frac{1}{2}\right)^{2} +\frac{3}{4} \ \\ Ta\ có\ :\ \left( x-\frac{1}{2}\right)^{2} \geqslant 0\ \\ \rightarrow \left( x-\frac{1}{2}\right)^{2} +\frac{3}{4} >0\ \\ Do\ đó\ P >0\ \\ \\ \end{array}$
