\(a,P=\left[\dfrac{1}{\sqrt{x}+1}-\dfrac{2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(x-1\right)}\right]:\dfrac{\sqrt{x}+1-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\left(x\ge0;x\ne1\right)\\ P=\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{2}{\left(\sqrt{x}+1\right)^2}\right)\cdot\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\\ P=\dfrac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)^2}\cdot\left(\sqrt{x}+1\right)=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\\ b,P=1\Leftrightarrow\sqrt{x}-1=\sqrt{x}+1\\ \Leftrightarrow0\sqrt{x}=2\Leftrightarrow x\in\varnothing\\ c,P>0\Leftrightarrow\dfrac{\sqrt{x}-1}{\sqrt{x}+1}>0\\ \Leftrightarrow\sqrt{x}-1>0\left(\sqrt{x}+1\ge1>0\right)\\ \Leftrightarrow x>1\)
