$$ \begin{aligned} \frac{7}{10} &= \frac{3}{x-5}&& \text{multiply ALL terms by } \color{blue}{ 10(x-5) }. \\[1 em]10(x-5)\cdot\frac{7}{10} &= 10(x-5)\cdot\frac{3}{x-5}&& \text{cancel out the denominators} \\[1 em]7x-35 &= 30&& \text{ move -35 to the right } \\[1 em]7x &= 30+35&& \\[1 em]7x &= 65&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{65}{7}&& \\[1 em] \end{aligned} $$

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