ĐKXĐ:...
\(A=1+\left(\frac{1}{1-a}-\frac{\sqrt{a}}{1-a\sqrt{a}}\right).\left(2a+\sqrt{a}-1\right)\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\right)\)
\(=1+\left(\frac{\sqrt{a}-1}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\left(1-\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}\right)\left(2\sqrt{a}-1\right)\left(\sqrt{a}+1\right).\frac{\sqrt{a}}{2\sqrt{a}-1}\)
\(=1+\left(\frac{-1}{\sqrt{a}+1}+\frac{\sqrt{a}}{a+\sqrt{a}+1}\right).\sqrt{a}\left(\sqrt{a}+1\right)\)
\(=1+\left(-1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{a+\sqrt{a}+1}\right).\sqrt{a}\)
\(=1+\left(\frac{-a-\sqrt{a}-1+a+\sqrt{a}}{a+\sqrt{a}+1}\right).\sqrt{a}\)
\(=1-\frac{\sqrt{a}}{a+\sqrt{a}+1}=\frac{a+\sqrt{a}+1-\sqrt{a}}{a+\sqrt{a}+1}=\frac{a+1}{a+\sqrt{a}+1}\)
