a: \(B=\dfrac{1}{2\sqrt{x}+1}-\dfrac{2}{1-4x}\)
\(=\dfrac{1}{2\sqrt{x}+1}+\dfrac{2}{\left(2\sqrt{x}-1\right)\cdot\left(2\sqrt{x}+1\right)}\)
\(=\dfrac{2\sqrt{x}-1+2}{\left(2\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}=\dfrac{2\sqrt{x}+1}{\left(2\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}=\dfrac{1}{2\sqrt{x}-1}\)
Khi x=4 thì \(B=\dfrac{1}{2\cdot2-1}=\dfrac{1}{3}\)
b: M=A:B
\(=\left(\dfrac{4\sqrt{x}}{2\sqrt{x}-1}+\dfrac{1}{\sqrt{x}-2x}\right):\dfrac{1}{2\sqrt{x}-1}\)
\(=\left(\dfrac{4\sqrt{x}}{2\sqrt{x}-1}-\dfrac{1}{\sqrt{x}\left(2\sqrt{x}-1\right)}\right)\cdot\dfrac{2\sqrt{x}-1}{1}\)
\(=\dfrac{4x-1}{\sqrt{x}\left(2\sqrt{x}-1\right)}\cdot\dfrac{2\sqrt{x}-1}{1}=\dfrac{4x-1}{\sqrt{x}}\)
c: M<0
=>\(\dfrac{4x-1}{\sqrt{x}}< 0\)
=>4x-1<0
=>x<1/4
Kết hợp ĐKXĐ, ta được: \(0< x< \dfrac{1}{4}\)
