\(ĐKXĐ:\dfrac{1+x}{2x-3}\ge0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}1+x\ge0\\2x-3>0\end{matrix}\right.\\\left\{{}\begin{matrix}1+x\le0\\2x-3< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge-1\\x>\dfrac{3}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x\le-1\\x< \dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{3}{2}\\x\le-1\end{matrix}\right.\)
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