$$\frac{4}{3\cdot(2+34)}-9\cdot(3+4\cdot5)+\frac{3+6\cdot(2+3)}{3+4\cdot6} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{4}{3\cdot(2+34)}-9\cdot(3+4\cdot5)+\frac{3+6\cdot(2+3)}{3+4\cdot6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 108 }. \\[1 em]108\cdot\frac{4}{3\cdot(2+34)}-108\cdot9\cdot(3+4\cdot5)+108\frac{3+6\cdot(2+3)}{3+4\cdot6} &= 108\cdot0&& \text{cancel out the denominators} \\[1 em]5184-22356+132 &= 0&& \text{simplify left side} \\[1 em]-17040 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ -17040 = 0 } $ is FALSE, we conclude that the equation has no solution.
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