$$ \begin{aligned} 3x-\frac{5}{4} &= 2x+\frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot3x-12\cdot\frac{5}{4} &= 12\cdot2x+12\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]36x-15 &= 24x+4&& \text{move the $ \color{blue}{ 24x } $ to the left side and $ \color{blue}{ -15 }$ to the right} \\[1 em]36x-24x &= 4+15&& \text{simplify left and right hand side} \\[1 em]12x &= 19&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{19}{12}&& \\[1 em] \end{aligned} $$

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