$$ \begin{aligned} \frac{5}{3x-1} &= 6\cdot\frac{3}{3x+4}&& \text{multiply ALL terms by } \color{blue}{ (3x-1)(3x+4) }. \\[1 em](3x-1)(3x+4)\cdot\frac{5}{3x-1} &= (3x-1)(3x+4)\cdot6\cdot\frac{3}{3x+4}&& \text{cancel out the denominators} \\[1 em]15x+20 &= 54x-18&& \text{move the $ \color{blue}{ 54x } $ to the left side and $ \color{blue}{ 20 }$ to the right} \\[1 em]15x-54x &= -18-20&& \text{simplify left and right hand side} \\[1 em]-39x &= -38&& \text{ divide both sides by $ -39 $ } \\[1 em]x &= \frac{-38}{-39}&& \\[1 em]x &= \frac{38}{39}&& \\[1 em] \end{aligned} $$

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