$$\frac{x}{x+2} = \frac{10}{15}$$

$$ \begin{aligned} \frac{x}{x+2} &= \frac{10}{15}&& \text{multiply ALL terms by } \color{blue}{ (x+2)\cdot15 }. \\[1 em](x+2)\cdot15 \cdot \frac{x}{x+2} &= (x+2)\cdot15\cdot\frac{10}{15}&& \text{cancel out the denominators} \\[1 em]15x &= 10x+20&& \text{move the $ \color{blue}{ 10x } $ to the left side} \\[1 em]15x-10x &= 20&& \text{simplify left side} \\[1 em]5x &= 20&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{20}{5}&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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