$$\frac{1}{24}+\frac{1}{15} = \frac{1}{x}$$

$$ \begin{aligned} \frac{1}{24}+\frac{1}{15} &= \frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ 24\cdot15x }. \\[1 em]24\cdot15x\cdot\frac{1}{24}+24\cdot15x\cdot\frac{1}{15} &= 24\cdot15x\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]15x+24x &= 360&& \text{simplify left side} \\[1 em]39x &= 360&& \text{ divide both sides by $ 39 $ } \\[1 em]x &= \frac{360}{39}&& \\[1 em]x &= \frac{120}{13}&& \\[1 em] \end{aligned} $$

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