Question

Rút gọn: \(A=\left(1+\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(1-\dfrac{a+2\sqrt{a}}{2+\sqrt{a}}\right)\)

Answer 1

\(A=\left(1+\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(1-\dfrac{a+2\sqrt{a}}{2+\sqrt{a}}\right)\left(dk:a\ge0,a\ne1\right)\)

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

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

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