Question
$$0x\cdot9-\frac{9}{9} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 0x\cdot9-\frac{9}{9} &= 0&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]90x\cdot9-9\cdot\frac{9}{9} &= 9\cdot0&& \text{cancel out the denominators} \\[1 em]0-9 &= 0&& \text{simplify left side} \\[1 em]-9 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ -9 = 0 } $ is FALSE, we conclude that the equation has no solution.
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