$$ \begin{aligned} \frac{2x-12}{x-3} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-3 }. \\[1 em](x-3)\frac{2x-12}{x-3} &= (x-3)\cdot0&& \text{cancel out the denominators} \\[1 em]2x-12 &= 0&& \text{ move the constants to the right } \\[1 em]2x &= 12&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{12}{2}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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