$$\frac{r}{r-1} = \frac{4}{r}$$
Answer
$$ r = 2 $$
Explanation
$$ \begin{aligned} \frac{r}{r-1} &= \frac{4}{r}&& \text{multiply ALL terms by } \color{blue}{ (r-1)r }. \\[1 em](r-1)r\frac{r}{r-1} &= (r-1)r\cdot\frac{4}{r}&& \text{cancel out the denominators} \\[1 em]r^2 &= 4r-4&& \text{move all terms to the left hand side } \\[1 em]r^2-4r+4 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-4x+4 = 0 $ is a quadratic equation.
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