$$ \begin{aligned} \frac{x}{2}+\frac{x}{3} &= \frac{1}{10}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{x}{2}+30\frac{x}{3} &= 30\cdot\frac{1}{10}&& \text{cancel out the denominators} \\[1 em]15x+10x &= 3&& \text{simplify left side} \\[1 em]25x &= 3&& \text{ divide both sides by $ 25 $ } \\[1 em]x &= \frac{3}{25}&& \\[1 em] \end{aligned} $$

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