Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$$r=-\frac{hv^2}{v^2-2gh}$$
Solving the equation for $r$ using the rules of Algebra, we obtain: $$v^2=\left(\sqrt{2gr}\sqrt{\frac{h}{r+h}}\right)^2\\ v^2=\frac{2ghr}{r+h}\\ r=-\frac{hv^2}{v^2-2gh}$$