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Algebraic substitution

by cristo
Tags: algebraic, substitution
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May13-07, 07:33 AM
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1. The problem statement, all variables and given/known data

I have this function [tex]F(r)=\frac{(r-r_+)(r-r_-)}{r^2}[/tex] and I want to make the subsitution [itex]r=r_+(1+\rho^2)[/itex].
2. Relevant equations


3. The attempt at a solution

So, I sub in, to obtain [tex]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}[/tex].

Now, the solutions say that this is equal to [tex]\frac{r_+\rho^2(r_+-r_-)}{r_+^2}\cdot [1+O(\rho^2)] [/tex], however I cannot, for the life of me, see how to get this from my line above! Can anyone help?
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May13-07, 07:50 AM
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Looks like a Taylor expansion to me, but I could be wrong...
May13-07, 08:01 AM
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P: 8,316
Quote Quote by Hootenanny View Post
Looks like a Taylor expansion to me, but I could be wrong...
Yup, you're correct. I never spot things like that. Thanks!

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