$$ \begin{aligned} \frac{21}{x+4} &= \frac{7}{x+2}&& \text{multiply ALL terms by } \color{blue}{ (x+4)(x+2) }. \\[1 em](x+4)(x+2)\cdot\frac{21}{x+4} &= (x+4)(x+2)\cdot\frac{7}{x+2}&& \text{cancel out the denominators} \\[1 em]21x+42 &= 7x+28&& \text{move the $ \color{blue}{ 7x } $ to the left side and $ \color{blue}{ 42 }$ to the right} \\[1 em]21x-7x &= 28-42&& \text{simplify left and right hand side} \\[1 em]14x &= -14&& \text{ divide both sides by $ 14 $ } \\[1 em]x &= -\frac{14}{14}&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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