$$ \begin{aligned} \frac{1}{12}+\frac{1}{r} &= \frac{1}{8}&& \text{multiply ALL terms by } \color{blue}{ 12r\cdot8 }. \\[1 em]12r\cdot8\cdot\frac{1}{12}+12r\cdot8\cdot\frac{1}{r} &= 12r\cdot8\cdot\frac{1}{8}&& \text{cancel out the denominators} \\[1 em]8r+96 &= 12r&& \text{move the $ \color{blue}{ 12r } $ to the left side and $ \color{blue}{ 96 }$ to the right} \\[1 em]8r-12r &= -96&& \text{simplify left side} \\[1 em]-4r &= -96&& \text{ divide both sides by $ -4 $ } \\[1 em]r &= \frac{-96}{-4}&& \\[1 em]r &= 24&& \\[1 em] \end{aligned} $$

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