$$ \begin{aligned} \frac{7}{4x}-\frac{3}{3x^2} &= \frac{1}{2x^2}&& \text{multiply ALL terms by } \color{blue}{ 4x\cdot3x^2\cdot2 }. \\[1 em]4x\cdot3x^2\cdot2\cdot\frac{7}{4x}-4x\cdot3x^2\cdot2\cdot\frac{3}{3x^2} &= 4x\cdot3x^2\cdot2\cdot\frac{1}{2x^2}&& \text{cancel out the denominators} \\[1 em]42-24x &= 12x&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 42 }$ to the right} \\[1 em]-24x-12x &= -42&& \text{simplify left side} \\[1 em]-36x &= -42&& \text{ divide both sides by $ -36 $ } \\[1 em]x &= \frac{-42}{-36}&& \\[1 em]x &= \frac{7}{6}&& \\[1 em] \end{aligned} $$

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