Question
$$\frac{1}{45}+\frac{1}{90} = \frac{1}{7}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{45}+\frac{1}{90} &= \frac{1}{7}&& \text{multiply ALL terms by } \color{blue}{ 630 }. \\[1 em]630\cdot\frac{1}{45}+630\cdot\frac{1}{90} &= 630\cdot\frac{1}{7}&& \text{cancel out the denominators} \\[1 em]14+7 &= 90&& \text{simplify left side} \\[1 em]21 &= 90&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 21 = 90 } $ is FALSE, we conclude that the equation has no solution.
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