\(P=\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x+2+x-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{2x+1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\)
\(x=25\Rightarrow P=\dfrac{\sqrt{25}}{25+\sqrt{25}+1}=\dfrac{5}{31}\)
\(\dfrac{1}{3}-P=\dfrac{1}{3}-\dfrac{\sqrt{x}}{x+\sqrt{x}+1}=\dfrac{x-2\sqrt{x}+1}{x+\sqrt{x}+1}=\dfrac{\left(\sqrt{x}-1\right)^2}{x+\sqrt{x}+1}>0\)
\(\Rightarrow P< \dfrac{1}{3}\)
