$$\frac{1}{x} = \frac{6}{x^2}$$

$$ \begin{aligned} \frac{1}{x} &= \frac{6}{x^2}&& \text{multiply ALL terms by } \color{blue}{ xx^2 }. \\[1 em]xx^2\cdot\frac{1}{x} &= xx^2\cdot\frac{6}{x^2}&& \text{cancel out the denominators} \\[1 em]1 &= \frac{6}{x^1}&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot1 &= x^1\cdot\frac{6}{x^1}&& \text{cancel out the denominators} \\[1 em]x &= 6&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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