$$\frac{1}{42}+\frac{1}{30} = \frac{1}{x}$$

$$ \begin{aligned} \frac{1}{42}+\frac{1}{30} &= \frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ 42\cdot30x }. \\[1 em]42\cdot30x\cdot\frac{1}{42}+42\cdot30x\cdot\frac{1}{30} &= 42\cdot30x\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]30x+42x &= 1260&& \text{simplify left side} \\[1 em]72x &= 1260&& \text{ divide both sides by $ 72 $ } \\[1 em]x &= \frac{1260}{72}&& \\[1 em]x &= \frac{35}{2}&& \\[1 em] \end{aligned} $$

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