Giải hệ bất phương trình \(\left\{{}\begin{matrix}\dfrac{4x+3}{2x-5}< 6\\\dfrac{x-1}{x+3}>2\end{matrix}\right.\) ta được nghiệm là
\(-3< x< \dfrac{5}{2}\).\(\dfrac{5}{2}< x< \dfrac{33}{8}\).\(-7< x< -3\).\(-3< x< \dfrac{33}{8}\).Hướng dẫn giải:\(\left\{{}\begin{matrix}\dfrac{4x+3}{2x-5}< 6\\\dfrac{x-1}{x+3}>2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4x+3}{2x-5}-6< 0\\\dfrac{x-1}{x+3}-2>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{-8+33}{2x-5}< 0\\\dfrac{-x-7}{x+3}>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x>\dfrac{33}{8}\\x< \dfrac{5}{2}\end{matrix}\right.\\-7< x< 3\end{matrix}\right.\Leftrightarrow\)\(-7< x< -3\)
