$$ \begin{aligned} \frac{5}{x}+3 &= \frac{2}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{5}{x}+x\cdot3 &= x\cdot\frac{2}{x}&& \text{cancel out the denominators} \\[1 em]5+3x &= 2&& \text{ move 5 to the right } \\[1 em]3x &= 2-5&& \\[1 em]3x &= -3&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{3}{3}&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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