$$\frac{6}{x-2} = \frac{7}{x}$$

$$ \begin{aligned} \frac{6}{x-2} &= \frac{7}{x}&& \text{multiply ALL terms by } \color{blue}{ (x-2)x }. \\[1 em](x-2)x\cdot\frac{6}{x-2} &= (x-2)x\cdot\frac{7}{x}&& \text{cancel out the denominators} \\[1 em]6x &= 7x-14&& \text{move the $ \color{blue}{ 7x } $ to the left side} \\[1 em]6x-7x &= -14&& \text{simplify left side} \\[1 em]-x &= -14&& \text{switch signs on both sides} \\[1 em]x &= 14&& \\[1 em] \end{aligned} $$

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