$$ \begin{aligned} \frac{5}{2}+\frac{3}{x} &= \frac{13}{x}&& \text{multiply ALL terms by } \color{blue}{ 2x }. \\[1 em]2x\cdot\frac{5}{2}+2x\cdot\frac{3}{x} &= 2x\cdot\frac{13}{x}&& \text{cancel out the denominators} \\[1 em]5x+6 &= 26&& \text{ move 6 to the right } \\[1 em]5x &= 26-6&& \\[1 em]5x &= 20&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{20}{5}&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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