Question
$$\frac{51}{2}-\frac{2}{3}+\frac{4}{9} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{51}{2}-\frac{2}{3}+\frac{4}{9} &= 0&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]18\cdot\frac{51}{2}-18\cdot\frac{2}{3}+18\cdot\frac{4}{9} &= 18\cdot0&& \text{cancel out the denominators} \\[1 em]459-12+8 &= 0&& \text{simplify left side} \\[1 em]455 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 455 = 0 } $ is FALSE, we conclude that the equation has no solution.
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