# Simplify an expression under certain condition

I have a variable A = g / (1 + g R) Actually, if the quantity (g R) >> 1 it is possible to write A as A ≈ 1/R. How can I do this in Mathematica? I tried with Assumptions, Refine, Simplify, but i can get the simplified form.

Thanks

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Have a look at Series. – b.gatessucks Jan 21 '14 at 16:42
Or a Limit. You have to prepare your expression so that the thing you want to make go to infinity/zero/whatever is a variable. – Rojo Jan 21 '14 at 17:12

If you rearrange the equation a bit, it is straightforward. Define a new variable x = g R. Then g = x/R and A = g/(1+g R) = (x/R)/(1+x). What you wish to calculate is the limit (as suggested by Rojo)

Limit[(x/R)/(1 + x), x -> Infinity]
1/R

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As b.gatessucks suggested in his comment above, this is a good spot for Series. You can get the Taylor series expansion of your expression about infinity as

Series[g/(1 + g R), {R, Infinity, 2}]


which yields the result

1/R-1/(g R^2)+O[1/R]^3


Now you only need adjust the number of terms in the series expansion to suit your purposes...

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Thanks you very much – luigi Jan 22 '14 at 19:05