Question
$$3(\frac{12}{10})^2 = 2(\frac{13}{10})^3$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3(\frac{12}{10})^2 &= 2(\frac{13}{10})^3&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot3(\frac{12}{10})^2 &= 10\cdot2(\frac{13}{10})^3&& \text{cancel out the denominators} \\[1 em]30 &= 40&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 30 = 40 } $ is FALSE, we conclude that the equation has no solution.
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