\(\dfrac{1}{3-5x}>\dfrac{1}{2x+3}\)
⇔ \(\dfrac{1}{3-5x}-\dfrac{1}{2x+3}>0\)
⇔ \(\dfrac{2x+3+5x-3}{\left(3-5x\right)\left(2x+3\right)}>0\)
⇔\(\dfrac{7x}{\left(3-5x\right)\left(2x+3\right)}>0\)
Lập bảng xét dấu , ta có :
Vậy , nghiệm của BPT là : x < \(\dfrac{-3}{2}\) hoặc : 0 < x < \(\dfrac{3}{5}\)
\(\dfrac{1}{3-5x}>\dfrac{1}{2x+3}\)
DKXD : \(x\ne\dfrac{3}{5};x\ne\dfrac{-3}{2}\)
\(\Leftrightarrow\dfrac{1}{3-5x}-\dfrac{1}{2x+3}>0\)
\(\Leftrightarrow\dfrac{2x+3}{\left(3-5x\right)\left(2x+3\right)}-\dfrac{3-5x}{\left(3-5x\right)\left(2x+3\right)}>0\)
\(\Leftrightarrow\dfrac{2x+3-3+5x}{\left(3-5x\right)\left(2x+3\right)}>0\)
\(\Leftrightarrow\dfrac{7x}{\left(3-5x\right)\left(2x+3\right)}>0\)
\(\Leftrightarrow7x>0\)
\(\Leftrightarrow x>0\)
Vậy bpt có nghiệm khi \(x>0\) tm \(x\ne\dfrac{3}{5};x\ne\dfrac{-3}{2}\)