\(\dfrac{2x}{2\sqrt[]{x}-1}-\dfrac{3}{2}\le0\left(x\ge0;x\ne\dfrac{1}{4}\right)\)
\(\Leftrightarrow\dfrac{4x-3\left(2\sqrt[]{x}-1\right)}{2\left(2\sqrt[]{x}-1\right)}\le0\)
\(\Leftrightarrow\dfrac{4x-6\sqrt[]{x}+3}{2\left(2\sqrt[]{x}-1\right)}\le0\)
\(\Leftrightarrow\dfrac{4x-6\sqrt[]{x}+3}{2\left(2\sqrt[]{x}-1\right)}\le0\)
\(\Leftrightarrow\dfrac{4\left(x-\dfrac{3}{2}\sqrt[]{x}+\dfrac{9}{16}\right)-\dfrac{9}{4}+3}{2\left(2\sqrt[]{x}-1\right)}\le0\)
\(\Leftrightarrow\dfrac{4\left(\sqrt[]{x}-\dfrac{3}{4}\right)^2+\dfrac{3}{4}}{2\left(2\sqrt[]{x}-1\right)}\le0\)
mà \(4\left(\sqrt[]{x}-\dfrac{3}{4}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}>0,\forall x\in R\)
\(pt\Leftrightarrow2\left(2\sqrt[]{x}-1\right)< 0\)
\(\Leftrightarrow\sqrt[]{x}< \dfrac{1}{2}\)
\(\Leftrightarrow x< \dfrac{1}{4}\)
mà \(x\ge0;x\ne\dfrac{1}{4}\)
\(pt\Leftrightarrow0\le x< \dfrac{1}{4}\)
