$$ \begin{aligned} \frac{3}{4} &= \frac{2}{3}c+\frac{3}{5}&& \text{multiply ALL terms by } \color{blue}{ 60 }. \\[1 em]60\cdot\frac{3}{4} &= 60 \cdot \frac{2}{3}c+60\cdot\frac{3}{5}&& \text{cancel out the denominators} \\[1 em]45 &= 40c+36&& \text{ swap the left and right side of the equation } \\[1 em]40c+36 &= 45&& \text{ move 36 to the right } \\[1 em]40c &= 45-36&& \\[1 em]40c &= 9&& \text{ divide both sides by $ 40 $ } \\[1 em]c &= \frac{9}{40}&& \\[1 em] \end{aligned} $$

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