$$ \begin{aligned} 8 \cdot \frac{x}{9-2x} &= 0&& \text{multiply ALL terms by } \color{blue}{ 9-2x }. \\[1 em](9-2x)\cdot8 \cdot \frac{x}{9-2x} &= (9-2x)\cdot0&& \text{cancel out the denominators} \\[1 em]8x &= 0&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{0}{8}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$
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