Question
$$\frac{1}{\frac{1}{175}+\frac{1}{50}} = r$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{\frac{1}{175}+\frac{1}{50}} &= r&& \text{multiply ALL terms by } \color{blue}{ 0 }. \\[1 em]0\cdot\frac{1}{\frac{1}{175}+\frac{1}{50}} &= 0r&& \text{cancel out the denominators} \\[1 em]1 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 1 = 0 } $ is FALSE, we conclude that the equation has no solution.
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