\(D=\dfrac{2\left|x\right|+3}{3\left|x\right|-1}\)
\(\left\{{}\begin{matrix}\left|x\right|\ge0\Rightarrow2\left|x\right|\ge0\Rightarrow2\left|x\right|+3\ge3\\\left|x\right|\ge0\Rightarrow3\left|x\right|\ge0\Rightarrow3\left|x\right|-1\ge-1\end{matrix}\right.\)
\(MAX_D\Rightarrow D\in Z^+\)
Chắc chắn: \(2\left|x\right|+3\in Z^+\)
\(\Rightarrow3\left|x\right|-1\in Z^+\)
\(MAX_D\Rightarrow MIN_{3\left|x\right|-1}\)
\(\Rightarrow3\left|x\right|-1=1\)
\(\Rightarrow3\left|x\right|=2\Rightarrow\left|x\right|=\dfrac{2}{3}\)
\(\Rightarrow MAX_D=\dfrac{2\left|\dfrac{2}{3}\right|+3}{3\left|\dfrac{2}{3}\right|-1}=\dfrac{\dfrac{13}{3}}{1}=\dfrac{13}{3}\)
