Question
$$6\cdot\frac{5}{8}-4\cdot\frac{1}{6} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 6\cdot\frac{5}{8}-4\cdot\frac{1}{6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24\cdot6\cdot\frac{5}{8}-24\cdot4\cdot\frac{1}{6} &= 24\cdot0&& \text{cancel out the denominators} \\[1 em]90-16 &= 0&& \text{simplify left side} \\[1 em]74 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 74 = 0 } $ is FALSE, we conclude that the equation has no solution.
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