Question

Rút gọn:

A= \(\left(\dfrac{1}{2\sqrt{x}-1}-\dfrac{2\sqrt{x}}{4x-1}\right):\dfrac{1}{8x-4\sqrt{x}}\)

Answer 1

điều kiện xác định : \(x\ge0;x\ne\dfrac{1}{4}\)

ta có : \(A=\left(\dfrac{1}{2\sqrt{x}-1}-\dfrac{2\sqrt{x}}{4x-1}\right):\dfrac{1}{8x-4\sqrt{x}}\)

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

\(\Leftrightarrow A=\left(\dfrac{2\sqrt{x}+1-2\sqrt{x}}{\left(2\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)}\right).\dfrac{4\sqrt{x}\left(2\sqrt{x}-1\right)}{1}\)

\(\Leftrightarrow A=\dfrac{4\sqrt{x}}{2\sqrt{x}+1}\)