ĐK: \(a\ge0;a\ne1\)
\(P=\dfrac{a\sqrt{a}}{\sqrt{a}-1}+\dfrac{1}{1-\sqrt{a}}\)
\(=\dfrac{a\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}-1}\)
\(=\dfrac{a\sqrt{a}-1}{\sqrt{a}-1}\)
\(=\dfrac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}-1}\)
\(=a+\sqrt{a}+1\)
Ta có: \(P=\dfrac{a\sqrt{a}}{\sqrt{a}-1}+\dfrac{1}{1-\sqrt{a}}=\dfrac{\left(\sqrt{a}\right)^3-1}{\sqrt{a}-1}=\dfrac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}-1}=a+\sqrt{a}+1\)
\(P=\dfrac{a\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}-1}=a+\sqrt{a}+1\)