Question
$$\frac{5^2}{6^2}-\frac{1}{3}(-\frac{2}{5}) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{5^2}{6^2}-\frac{1}{3}(-\frac{2}{5}) &= 0&& \text{multiply ALL terms by } \color{blue}{ 180 }. \\[1 em]180 \cdot \frac{5^2}{6^2}-180\frac{1}{3}(-\frac{2}{5}) &= 180\cdot0&& \text{cancel out the denominators} \\[1 em]125-(-24) &= 0&& \text{simplify left side} \\[1 em]125+24 &= 0&& \\[1 em]149 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 149 = 0 } $ is FALSE, we conclude that the equation has no solution.
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