$$\frac{12}{x-4} = 9$$

$$ \begin{aligned} \frac{12}{x-4} &= 9&& \text{multiply ALL terms by } \color{blue}{ x-4 }. \\[1 em](x-4)\cdot\frac{12}{x-4} &= (x-4)\cdot9&& \text{cancel out the denominators} \\[1 em]12 &= 9x-36&& \text{ swap the left and right side of the equation } \\[1 em]9x-36 &= 12&& \text{ move -36 to the right } \\[1 em]9x &= 12+36&& \\[1 em]9x &= 48&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{48}{9}&& \\[1 em]x &= \frac{16}{3}&& \\[1 em] \end{aligned} $$

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