Factor out the common term \(3\).
\[\frac{1}{3(2x-1)}+\frac{3}{2x-1}\times \frac{2}{3}=0\]
Cancel \(3\).
\[\frac{1}{3(2x-1)}+\frac{1}{2x-1}\times 2=0\]
Simplify \(\frac{1}{2x-1}\times 2\) to \(\frac{2}{2x-1}\).
\[\frac{1}{3(2x-1)}+\frac{2}{2x-1}=0\]
Simplify \(\frac{1}{3(2x-1)}+\frac{2}{2x-1}\) to \(\frac{7}{3(2x-1)}\).
\[\frac{7}{3(2x-1)}=0\]
Multiply both sides by \(3(2x-1)\).
\[7=0\]
Since \(7=0\) is false, there is no solution.
[No Solution]
