(3x-5)(3-5x)>0
=>(3x-5)(5x-3)<0
TH1: \(\left\{{}\begin{matrix}3x-5< 0\\5x-3>0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< \dfrac{5}{3}\\x>\dfrac{3}{5}\end{matrix}\right.\Leftrightarrow\dfrac{3}{5}< x< \dfrac{5}{3}\)
TH2: \(\left\{{}\begin{matrix}3x-5>0\\5x-3< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>\dfrac{5}{3}\\x< \dfrac{3}{5}\end{matrix}\right.\)
=>\(x\in\varnothing\)
\(\left(3x-5\right)\left(3-5x\right)>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x-5>0\\3-5x>0\end{matrix}\right.\\\left\{{}\begin{matrix}3x-5< 0\\3-5x< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x>5\\-5x>-3\end{matrix}\right.\\\left\{{}\begin{matrix}3x< 5\\-5x< 3\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\dfrac{5}{3}\\x< \dfrac{3}{5}\end{matrix}\right.\\\left\{{}\begin{matrix}x< \dfrac{5}{3}\\x>\dfrac{3}{5}\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{5}{3}< x< \dfrac{3}{5}\left(loại\right)\\\dfrac{3}{5}< x< \dfrac{5}{3}\end{matrix}\right.\)
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