$$\frac{3}{4}+\frac{1}{2x} = \frac{1}{2x}+\frac{1}{3x^2}$$

$$ \begin{aligned} \frac{3}{4}+\frac{1}{2x} &= \frac{1}{2x}+\frac{1}{3x^2}&& \text{multiply ALL terms by } \color{blue}{ 4\cdot2x\cdot3x^2 }. \\[1 em]4\cdot2x\cdot3x^2\cdot\frac{3}{4}+4\cdot2x\cdot3x^2\cdot\frac{1}{2x} &= 4\cdot2x\cdot3x^2\cdot\frac{1}{2x}+4\cdot2x\cdot3x^2\cdot\frac{1}{3x^2}&& \text{cancel out the denominators} \\[1 em]18x+12 &= 12+8x&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]18x-8x &= 12-12&& \text{simplify left and right hand side} \\[1 em]10x &= 0&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{0}{10}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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