$$ \begin{aligned} \frac{x}{5}-\frac{x}{6} &= \frac{3}{8}&& \text{multiply ALL terms by } \color{blue}{ 120 }. \\[1 em]120 \cdot \frac{x}{5}-120\frac{x}{6} &= 120\cdot\frac{3}{8}&& \text{cancel out the denominators} \\[1 em]24x-20x &= 45&& \text{simplify left side} \\[1 em]4x &= 45&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{45}{4}&& \\[1 em] \end{aligned} $$

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