$$\frac{1}{3}x+\frac{4}{5}x-\frac{1}{4}x = \frac{53}{12}$$

$$ \begin{aligned} \frac{1}{3}x+\frac{4}{5}x-\frac{1}{4}x &= \frac{53}{12}&& \text{multiply ALL terms by } \color{blue}{ 60 }. \\[1 em]60 \cdot \frac{1}{3}x+60\frac{4}{5}x-60\frac{1}{4}x &= 60\cdot\frac{53}{12}&& \text{cancel out the denominators} \\[1 em]20x+48x-15x &= 265&& \text{simplify left side} \\[1 em]53x &= 265&& \text{ divide both sides by $ 53 $ } \\[1 em]x &= \frac{265}{53}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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