$$\frac{n}{n}-3 = \frac{2}{3}$$

$$ \begin{aligned} \frac{n}{n}-3 &= \frac{2}{3}&& \text{multiply ALL terms by } \color{blue}{ n\cdot3 }. \\[1 em]n\cdot3 \cdot \frac{n}{n}-n\cdot3\cdot3 &= n\cdot3\cdot\frac{2}{3}&& \text{cancel out the denominators} \\[1 em]3n-9n &= 2n&& \text{simplify left side} \\[1 em]-6n &= 2n&& \text{move the $ \color{blue}{ 2n } $ to the left side} \\[1 em]-6n-2n &= 0&& \text{simplify left side} \\[1 em]-8n &= 0&& \text{ divide both sides by $ -8 $ } \\[1 em]n &= \frac{0}{-8}&& \\[1 em]n &= 0&& \\[1 em] \end{aligned} $$

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