1. **State the problem:** Solve for $r$ in the equation $x = \frac{r+1}{r}$. 2. **Rewrite the equation:** Multiply both sides by $r$ to eliminate the denominator: $$xr = r + 1$$ 3. **Rearrange terms:** Move all terms to one side: $$xr - r = 1$$ 4. **Factor out $r$:** $$r(x - 1) = 1$$ 5. **Solve for $r$:** Divide both sides by $(x - 1)$: $$r = \frac{1}{x - 1}$$ 6. **Express as a root if needed:** Since $r$ is already isolated, no root extraction is necessary here. **Final answer:** $$r = \frac{1}{x - 1}$$