\(a,\dfrac{2x-7}{x+3}>1\)
\(\Leftrightarrow\dfrac{2x-7}{x+3}-1>0\)
\(\Leftrightarrow\dfrac{2x-7-x-3}{x+3}>0\)
\(\Leftrightarrow\dfrac{x-10}{x+3}>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-10>0\\x+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-10< 0\\x+3< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>10\\x>-3\end{matrix}\right.\\\left\{{}\begin{matrix}x\backslash< 10\\x< -3\end{matrix}\right.\end{matrix}\right.\)
Vậy x ∈ ( - ∞;-3) \(\cup\) ( 10; ∞ )
\(b,\dfrac{4x+7}{5-x}\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}4x+7>0\\5-x>0\end{matrix}\right.\\\left\{{}\begin{matrix}4x+7< 0\\5-x< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-\dfrac{7}{4}\\x< 5\end{matrix}\right.\\\left\{{}\begin{matrix}x< -\dfrac{7}{4}\\x>5\end{matrix}\right.\end{matrix}\right.\)
TH2 : vô nghiệm
Vậy bpt có nghiệm \(-\dfrac{7}{4}< x< 5\)
