$$\frac{7}{2a-3} = \frac{4}{a}$$

$$ \begin{aligned} \frac{7}{2a-3} &= \frac{4}{a}&& \text{multiply ALL terms by } \color{blue}{ (2a-3)a }. \\[1 em](2a-3)a\cdot\frac{7}{2a-3} &= (2a-3)a\cdot\frac{4}{a}&& \text{cancel out the denominators} \\[1 em]7a &= 8a-12&& \text{move the $ \color{blue}{ 8a } $ to the left side} \\[1 em]7a-8a &= -12&& \text{simplify left side} \\[1 em]-a &= -12&& \text{switch signs on both sides} \\[1 em]a &= 12&& \\[1 em] \end{aligned} $$

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