$$\frac{9}{x} = \frac{18}{x^2}$$

$$ \begin{aligned} \frac{9}{x} &= \frac{18}{x^2}&& \text{multiply ALL terms by } \color{blue}{ xx^2 }. \\[1 em]xx^2\cdot\frac{9}{x} &= xx^2\cdot\frac{18}{x^2}&& \text{cancel out the denominators} \\[1 em]9 &= \frac{18}{x^1}&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot9 &= x^1\cdot\frac{18}{x^1}&& \text{cancel out the denominators} \\[1 em]9x &= 18&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{18}{9}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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