\(A=\left(\dfrac{a+1-2\sqrt{a}}{a+1}\right):\left(\dfrac{1}{\sqrt{a}+1}-\dfrac{2\sqrt{a}}{\left(\sqrt{a}+1\right)\left(a+1\right)}\right)\)
\(=\left(\dfrac{\left(\sqrt{a}-1\right)^2}{a+1}\right):\left(\dfrac{a+1}{\left(\sqrt{a}+1\right)\left(a+1\right)}-\dfrac{2\sqrt{a}}{\left(\sqrt{a}+1\right)\left(a+1\right)}\right)\)
\(=\dfrac{\left(\sqrt{a}-1\right)^2}{a+1}:\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(a+1\right)}=\dfrac{\left(\sqrt{a}-1\right)^2\left(\sqrt{a}+1\right)\left(a+1\right)}{\left(a+1\right)\left(\sqrt{a}-1\right)^2}\)
\(=\sqrt{a}+1\)
Với \(a=2011-2\sqrt{2010}=2010-2\sqrt{2010}+1=\left(\sqrt{2010}-1\right)^2\)
\(\Rightarrow P=\sqrt{\left(\sqrt{2010}-1\right)^2}+1=\left|\sqrt{2010}-1\right|+1=\sqrt{2010}-1+1=\sqrt{2010}\)
