a: \(A=1-\left(\dfrac{2}{2\sqrt{x}+1}-\dfrac{5\sqrt{x}}{4x-1}+\dfrac{1}{2\sqrt{x}-1}\right):\dfrac{\sqrt{x}-1}{4x+4\sqrt{x}+1}\)
\(=1-\dfrac{4\sqrt{x}-2-5\sqrt{x}+2\sqrt{x}+1}{4x-1}\cdot\dfrac{\left(2\sqrt{x}+1\right)^2}{\sqrt{x}-1}\)
\(=1-\dfrac{2\sqrt{x}+1}{2\sqrt{x}-1}\)
\(=\dfrac{2\sqrt{x}-1-2\sqrt{x}-1}{2\sqrt{x}-1}=\dfrac{-2}{2\sqrt{x}-1}\)
b: Để \(A>\dfrac{1-2\sqrt{x}}{2}\) thì \(\dfrac{-2}{2\sqrt{x}-1}-\dfrac{1-2\sqrt{x}}{2}>0\)
\(\Leftrightarrow\dfrac{-2}{2\sqrt{x}-1}+\dfrac{2\sqrt{x}-1}{2}>0\)
\(\Leftrightarrow\dfrac{-4+4x-4\sqrt{x}+1}{2\left(2\sqrt{x}-1\right)}>0\)
\(\Leftrightarrow\dfrac{\left(2\sqrt{x}-1\right)^2-4}{2\left(2\sqrt{x}-1\right)}>0\)
\(\Leftrightarrow\dfrac{2\sqrt{x}-3}{2\sqrt{x}-1}>0\)
=>x>9/4 hoặc 0<x<1/4
a: =1−4√x−2−5√x+2√x+14x−1⋅(2√x+1)2√x−1=1−4x−2−5x+2x+14x−1⋅(2x+1)2x−1
=2√x−1−2√x−12√x−1=−22√x−1=2x−1−2x−12x−1=−22x−1
b: Để −22√x−1−1−2√x2>0−22x−1−1−2x2>0
⇔−4+4x−4√x+12(2√x−1)>0⇔−4+4x−4x+12(2x−1)>0
⇔2√x−32√x−1>0⇔2x−32x−1>0
=>x>9/4 hoặc 0<x<1/4