Question

[Dương Tất Đạt]

Q = \(\left(1-\dfrac{\sqrt{a}-4a}{1-4a}\right)\) : \(\left[1-\dfrac{1+2a-2\sqrt{a}\left(2\sqrt{a}+1\right)}{1-4a}\right]\) với a > 0, a ≠ \(\dfrac{1}{4}\)

Rút gọn

Giúp em với ạ ! Em cảm ơn !

Answer 1

[Zen Ryder]

Q = (1 - \(\dfrac{\sqrt{a}-4a}{1-4a}\)_{) : \(\left[1-\dfrac{1+2a-2\sqrt{a}\left(2\sqrt{a}+1\right)}{1-4a}\right]\)}

     _{= \(\left(\dfrac{1-4a-\sqrt{a}+4a}{1-4a}\right):\left[\dfrac{1-4a-1-2a+4a+2\sqrt{a}}{1-4a}\right]\)}

    = \(\dfrac{1-\sqrt{a}}{1-4a}:\left(\dfrac{-2a+2\sqrt{a}}{1-4a}\right)\)

    = \(\dfrac{1-\sqrt{a}}{1-4a}.\dfrac{1-4a}{2\sqrt{a}\left(1-\sqrt{a}\right)}\)

    = \(\dfrac{1}{2\sqrt{a}}\) = \(\dfrac{\sqrt{a}}{2a}\)