# Algebraic substitution

by cristo
Tags: algebraic, substitution
 Mentor P: 8,316 1. The problem statement, all variables and given/known data I have this function $$F(r)=\frac{(r-r_+)(r-r_-)}{r^2}$$ and I want to make the subsitution $r=r_+(1+\rho^2)$. 2. Relevant equations None. 3. The attempt at a solution So, I sub in, to obtain $$F=\frac{[r_+(1+\rho^2)-r_-][r_+(1+\rho^2)-r_-]}{r_+^2(1+\rho^2)^2}=\frac{\rho^2[r_+(1+\rho^2)-r_-]}{r_+^2(1+\rho^2)^2}$$. Now, the solutions say that this is equal to $$\frac{r_+\rho^2(r_+-r_-)}{r_+^2}\cdot [1+O(\rho^2)]$$, however I cannot, for the life of me, see how to get this from my line above! Can anyone help?