Rút gọn biểu thức: \(\left ( \dfrac{1-a\sqrt{a}}{1-\sqrt{a}} +\sqrt{a}\right ). \left ( \dfrac{1-\sqrt{a}}{1-a} \right )^{2}\) với \(a ≥ 0\) và \(a ≠ 1\)

* Hướng dẫn giải

Ta có: 

\(\left ( \dfrac{1-a\sqrt{a}}{1-\sqrt{a}} +\sqrt{a}\right ). \left ( \dfrac{1-\sqrt{a}}{1-a} \right )^{2}\)

\(=\left ( \dfrac{1-(\sqrt{a})^3}{1-\sqrt{a}} +\sqrt{a}\right ). \left ( \dfrac{1-\sqrt{a}}{(1-\sqrt a)(1+ \sqrt a)} \right )^{2}\)

\(=\left ( \dfrac{(1-\sqrt{a})(1+\sqrt a+(\sqrt a)^2)}{1-\sqrt{a}} +\sqrt{a}\right ). \left ( \dfrac{1}{1+ \sqrt a} \right )^{2}\)

\(=\left [ (1+\sqrt a+(\sqrt a)^2) +\sqrt{a}\right ].  \dfrac{1}{(1+ \sqrt a)^2}\)

\(=\left [ (1+2\sqrt a+(\sqrt a)^2)\right ].  \dfrac{1}{(1+ \sqrt a)^2}\)

\(=(1+\sqrt a)^2.  \dfrac{1}{(1+ \sqrt a)^2}=1\).