\(\dfrac{3x-2}{6}-\dfrac{2x+1}{5}=\dfrac{x-3}{2}-\dfrac{x-1}{3}\\ \dfrac{5\left(3x-2\right)}{30}-\dfrac{6\left(2x+1\right)}{30}=\dfrac{15\left(x-3\right)}{30}-\dfrac{10\left(x-1\right)}{30}\\ 5\left(3x-2\right)-6\left(2x+1\right)=15\left(x-3\right)-10\left(x-1\right)\\ 15x-10-12x-6=15x-45-10x+10\\ 3x-16=5x-35\\ 5x-3x=-16+35\\ 2x=19\\ x=\dfrac{19}{2}\)
\(\dfrac{3x-2}{6}-\dfrac{2x+1}{5}=\dfrac{x-3}{2}-\dfrac{x-1}{3}\)
=>\(\dfrac{5\left(3x-2\right)-6\left(2x+1\right)}{30}=\dfrac{15\left(x-3\right)-10\left(x-1\right)}{30}\)
=>\(5\left(3x-2\right)-6\left(2x+1\right)=15\left(x-3\right)-10\left(x-1\right)\)
=>\(15x-10-12x-6=15x-45-10x+10\)
=>3x-16=5x-35
=>-2x=-35+16=-19
=>\(x=\dfrac{19}{2}\)
