$$\frac{4}{x} = \frac{8}{x+2}$$

$$ \begin{aligned} \frac{4}{x} &= \frac{8}{x+2}&& \text{multiply ALL terms by } \color{blue}{ x(x+2) }. \\[1 em]x(x+2)\cdot\frac{4}{x} &= x(x+2)\cdot\frac{8}{x+2}&& \text{cancel out the denominators} \\[1 em]4x+8 &= 8x&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 8 }$ to the right} \\[1 em]4x-8x &= -8&& \text{simplify left side} \\[1 em]-4x &= -8&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-8}{-4}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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