\(\dfrac{1}{x}+\dfrac{3}{2x}-\dfrac{5}{24}=0\)
\(\Leftrightarrow24+36-5x=0\)
\(\Leftrightarrow5x=60\)
\(\Leftrightarrow x=12\)
\(\dfrac{x-5}{3}+\dfrac{x+1}{2}>3\)
\(\Leftrightarrow2x-10+3x+3>18\)
\(\Leftrightarrow5x>25\)
\(\Leftrightarrow x>5\)
\(\dfrac{2}{x-1}+\dfrac{1}{x+2}=\dfrac{2x}{\left(x+2\right)\left(x-1\right)}\)
\(\Leftrightarrow2x+4+x-1=2x\)
\(\Leftrightarrow x=-3\)