\(a.\dfrac{4}{x+1}>0\)
\(\Leftrightarrow x+1>0\)
\(\Leftrightarrow x>-1\)
\(b.\dfrac{-5}{-x+2}< 0\)
\(\Leftrightarrow-x+2>0\)
\(\Leftrightarrow x< 2\)
\(c.\dfrac{x-3}{-3}< 0\)
\(\Leftrightarrow x-3>0\)
\(\Leftrightarrow x>3\)
\(d.\dfrac{x+1}{4}\ge0\)
\(\Leftrightarrow x+1\ge0\)
\(\Leftrightarrow x\ge-1\)
\(e.\dfrac{x+2}{x-3}>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2>0\\x-3>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+2< 0\\x-3< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-2\\x>3\end{matrix}\right.\\\left\{{}\begin{matrix}x< -2\\x< 3\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>3\\x< -2\end{matrix}\right.\)
\(f.\dfrac{2x-5}{1-3x}< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-5>0\\1-3x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-5< 0\\1-3x>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\dfrac{5}{2}\\x>\dfrac{1}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x< \dfrac{5}{2}\\x< \dfrac{1}{3}\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{5}{2}\\x< \dfrac{1}{3}\end{matrix}\right.\)
