ĐKXĐ: \(a\ge 0,a\ne 1\)
\(P=(\dfrac{1-a\sqrt a}{1-\sqrt a}+\sqrt a).(\dfrac{1+a\sqrt a}{1+\sqrt a}-\sqrt a)\\=(\dfrac{1-(\sqrt a)^2}{1-\sqrt a}+\sqrt a).(\dfrac{1+(\sqrt a)^2}{1+\sqrt a}-\sqrt a)\\=\dfrac{(1-\sqrt a)(1+\sqrt a+a)}{1-\sqrt a}+\sqrt a).(\dfrac{(1+\sqrt a)(1-\sqrt a+a)}{1+\sqrt a}-\sqrt a)\\=(1+\sqrt a+a+\sqrt a)(1-\sqrt a+a-\sqrt a)\\=(a+2\sqrt a+1)(a-2\sqrt a+1)\\=(\sqrt a+1)^2.(\sqrt a-1)^2\\=[(\sqrt a+1)(\sqrt a-1)]^2\\=(a-1)^2\)
Vậy \(P=(a-1)^2\)
