$$ \begin{aligned} \frac{a}{9}-\frac{a}{5} &= -\frac{8}{3}&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45 \cdot \frac{a}{9}-45\frac{a}{5} &= -45\cdot\frac{8}{3}&& \text{cancel out the denominators} \\[1 em]5a-9a &= -120&& \text{simplify left side} \\[1 em]-4a &= -120&& \text{ divide both sides by $ -4 $ } \\[1 em]a &= \frac{-120}{-4}&& \\[1 em]a &= 30&& \\[1 em] \end{aligned} $$

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