$$ \begin{aligned} \frac{\frac{\frac{2}{1}}{3}}{5}x+\frac{1}{4}+\frac{5}{6}x-2 &= 0&& \text{multiply ALL terms by } \color{blue}{ 60 }. \\[1 em]60 \cdot \frac{\frac{\frac{2}{1}}{3}}{5}x+60\cdot\frac{1}{4}+60\frac{5}{6}x-60\cdot2 &= 60\cdot0&& \text{cancel out the denominators} \\[1 em]8x+15+50x-120 &= 0&& \text{simplify left side} \\[1 em]58x-105 &= 0&& \text{ move the constants to the right } \\[1 em]58x &= 105&& \text{ divide both sides by $ 58 $ } \\[1 em]x &= \frac{105}{58}&& \\[1 em] \end{aligned} $$

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