$$ \begin{aligned} \frac{3}{x}+2 &= \frac{7}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{3}{x}+x\cdot2 &= x\cdot\frac{7}{x}&& \text{cancel out the denominators} \\[1 em]3+2x &= 7&& \text{ move 3 to the right } \\[1 em]2x &= 7-3&& \\[1 em]2x &= 4&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{4}{2}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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