Question
$$5\cdot\frac{2}{5}-3\cdot\frac{2}{3} = 1\cdot\frac{11}{15}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 5\cdot\frac{2}{5}-3\cdot\frac{2}{3} &= 1\cdot\frac{11}{15}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15\cdot5\cdot\frac{2}{5}-15\cdot3\cdot\frac{2}{3} &= 15\cdot1\cdot\frac{11}{15}&& \text{cancel out the denominators} \\[1 em]30-30 &= 11&& \text{simplify left side} \\[1 em]0 &= 11&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 11 } $ is FALSE, we conclude that the equation has no solution.
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