$$ \begin{aligned} \frac{2x-5}{x^2-8x+12} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2-8x+12 }. \\[1 em](x^2-8x+12)\frac{2x-5}{x^2-8x+12} &= (x^2-8x+12)\cdot0&& \text{cancel out the denominators} \\[1 em]2x-5 &= 0&& \text{ move the constants to the right } \\[1 em]2x &= 5&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{5}{2}&& \\[1 em] \end{aligned} $$

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