$$\frac{1}{x-1} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{x-1} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-1 }. \\[1 em](x-1)\cdot\frac{1}{x-1} &= (x-1)\cdot0&& \text{cancel out the denominators} \\[1 em]1 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 1 = 0 } $ is FALSE, we conclude that the equation has no solution.
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