$$\frac{1}{x-3} = 10$$

$$ \begin{aligned} \frac{1}{x-3} &= 10&& \text{multiply ALL terms by } \color{blue}{ x-3 }. \\[1 em](x-3)\cdot\frac{1}{x-3} &= (x-3)\cdot10&& \text{cancel out the denominators} \\[1 em]1 &= 10x-30&& \text{ swap the left and right side of the equation } \\[1 em]10x-30 &= 1&& \text{ move -30 to the right } \\[1 em]10x &= 1+30&& \\[1 em]10x &= 31&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{31}{10}&& \\[1 em] \end{aligned} $$

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