$$\frac{4}{3\cdot(2+34)}-9\cdot(3+4\cdot5)+\frac{3+6\cdot(2+3)}{3+4\cdot6} = x$$

$$ \begin{aligned} \frac{4}{3\cdot(2+34)}-9\cdot(3+4\cdot5)+\frac{3+6\cdot(2+3)}{3+4\cdot6} &= x&& \text{multiply ALL terms by } \color{blue}{ 108 }. \\[1 em]108\cdot\frac{4}{3\cdot(2+34)}-108\cdot9\cdot(3+4\cdot5)+108\frac{3+6\cdot(2+3)}{3+4\cdot6} &= 108x&& \text{cancel out the denominators} \\[1 em]5184-22356+132 &= 108x&& \text{simplify left side} \\[1 em]-17040 &= 108x&& \text{ swap the left and right side of the equation } \\[1 em]108x &= -17040&& \text{ divide both sides by $ 108 $ } \\[1 em]x &= -\frac{17040}{108}&& \\[1 em]x &= -\frac{1420}{9}&& \\[1 em] \end{aligned} $$

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