$$\frac{1}{3}+\frac{4}{5} = \frac{x}{9}$$

$$ \begin{aligned} \frac{1}{3}+\frac{4}{5} &= \frac{x}{9}&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45\cdot\frac{1}{3}+45\cdot\frac{4}{5} &= 45 \cdot \frac{x}{9}&& \text{cancel out the denominators} \\[1 em]15+36 &= 5x&& \text{simplify left side} \\[1 em]51 &= 5x&& \text{ swap the left and right side of the equation } \\[1 em]5x &= 51&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{51}{5}&& \\[1 em] \end{aligned} $$

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