$$ \begin{aligned} 9 &= \frac{v+4}{v+12}&& \text{multiply ALL terms by } \color{blue}{ v+12 }. \\[1 em](v+12)\cdot9 &= (v+12)\frac{v+4}{v+12}&& \text{cancel out the denominators} \\[1 em]9v+108 &= v+4&& \text{move the $ \color{blue}{ v } $ to the left side and $ \color{blue}{ 108 }$ to the right} \\[1 em]9v-v &= 4-108&& \text{simplify left and right hand side} \\[1 em]8v &= -104&& \text{ divide both sides by $ 8 $ } \\[1 em]v &= -\frac{104}{8}&& \\[1 em]v &= -13&& \\[1 em] \end{aligned} $$

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