$$ \begin{aligned} \frac{x}{2}+\frac{x}{9} &= \frac{9}{4}&& \text{multiply ALL terms by } \color{blue}{ 36 }. \\[1 em]36 \cdot \frac{x}{2}+36\frac{x}{9} &= 36\cdot\frac{9}{4}&& \text{cancel out the denominators} \\[1 em]18x+4x &= 81&& \text{simplify left side} \\[1 em]22x &= 81&& \text{ divide both sides by $ 22 $ } \\[1 em]x &= \frac{81}{22}&& \\[1 em] \end{aligned} $$

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