$$ \begin{aligned} \frac{2}{4} &= \frac{7}{x}+9&& \text{multiply ALL terms by } \color{blue}{ 4x }. \\[1 em]4x\cdot\frac{2}{4} &= 4x\cdot\frac{7}{x}+4x\cdot9&& \text{cancel out the denominators} \\[1 em]2x &= 28+36x&& \text{move the $ \color{blue}{ 36x } $ to the left side} \\[1 em]2x-36x &= 28&& \text{simplify left side} \\[1 em]-34x &= 28&& \text{ divide both sides by $ -34 $ } \\[1 em]x &= -\frac{28}{34}&& \\[1 em]x &= -\frac{14}{17}&& \\[1 em] \end{aligned} $$

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