Question

Tìm đk có nghĩa của bt và rút gọn

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

Answer 1

ĐKXĐ: \(a\ge0;a\ne1\) Rút gọn: \(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1-\sqrt{a}}{1-a}\right)=\dfrac{1-a\sqrt{a}+\sqrt{a}-a}{1-\sqrt{a}}.\dfrac{1-\sqrt{a}}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}=\dfrac{\left(1-a\right)+\sqrt{a}\left(1-a\right)}{1-\sqrt{a}}.\dfrac{1}{1+\sqrt{a}}=\dfrac{\left(1-a\right)\left(1+\sqrt{a}\right)}{1-a}=1+\sqrt{a}\)