$$\frac{5}{r}-9 = \frac{8}{r}+5$$

$$ \begin{aligned} \frac{5}{r}-9 &= \frac{8}{r}+5&& \text{multiply ALL terms by } \color{blue}{ r }. \\[1 em]r\cdot\frac{5}{r}-r\cdot9 &= r\cdot\frac{8}{r}+r\cdot5&& \text{cancel out the denominators} \\[1 em]5-9r &= 8+5r&& \text{move the $ \color{blue}{ 5r } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]-9r-5r &= 8-5&& \text{simplify left and right hand side} \\[1 em]-14r &= 3&& \text{ divide both sides by $ -14 $ } \\[1 em]r &= -\frac{3}{14}&& \\[1 em] \end{aligned} $$

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