$$ \begin{aligned} \frac{7x+4}{x-6} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-6 }. \\[1 em](x-6)\frac{7x+4}{x-6} &= (x-6)\cdot0&& \text{cancel out the denominators} \\[1 em]7x+4 &= 0&& \text{ move the constants to the right } \\[1 em]7x &= -4&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= -\frac{4}{7}&& \\[1 em] \end{aligned} $$

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