$$\frac{2}{x} = \frac{9}{x-3}$$

$$ \begin{aligned} \frac{2}{x} &= \frac{9}{x-3}&& \text{multiply ALL terms by } \color{blue}{ x(x-3) }. \\[1 em]x(x-3)\cdot\frac{2}{x} &= x(x-3)\cdot\frac{9}{x-3}&& \text{cancel out the denominators} \\[1 em]2x-6 &= 9x&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]2x-9x &= 6&& \text{simplify left side} \\[1 em]-7x &= 6&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= -\frac{6}{7}&& \\[1 em] \end{aligned} $$

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