Question
$$1+2-3\cdot\frac{4}{5}+6-7\cdot\frac{8}{9} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 1+2-3\cdot\frac{4}{5}+6-7\cdot\frac{8}{9} &= 0&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45\cdot1+45\cdot2-45\cdot3\cdot\frac{4}{5}+45\cdot6-45\cdot7\cdot\frac{8}{9} &= 45\cdot0&& \text{cancel out the denominators} \\[1 em]45+90-108+270-280 &= 0&& \text{simplify left side} \\[1 em]17 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 17 = 0 } $ is FALSE, we conclude that the equation has no solution.
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