$$ \begin{aligned} \frac{1}{6}x^2 &= \frac{1}{3}x^2-\frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ 6\cdot3x }. \\[1 em]6\cdot3x \cdot \frac{1}{6}x^2 &= 6\cdot3x \cdot \frac{1}{3}x^2-6\cdot3x\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]3x &= 6x-18&& \text{move the $ \color{blue}{ 6x } $ to the left side} \\[1 em]3x-6x &= -18&& \text{simplify left side} \\[1 em]-3x &= -18&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{-18}{-3}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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