$$\frac{5}{x+2} = \frac{3}{x}$$

$$ \begin{aligned} \frac{5}{x+2} &= \frac{3}{x}&& \text{multiply ALL terms by } \color{blue}{ (x+2)x }. \\[1 em](x+2)x\cdot\frac{5}{x+2} &= (x+2)x\cdot\frac{3}{x}&& \text{cancel out the denominators} \\[1 em]5x &= 3x+6&& \text{move the $ \color{blue}{ 3x } $ to the left side} \\[1 em]5x-3x &= 6&& \text{simplify left side} \\[1 em]2x &= 6&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{6}{2}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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