How can I eliminate a parameter by substitution and simplification?

I have this equation

k = (a b c t)/(Sqrt[(f + t)^2])


and I want to set

p = t/(t + f)


In which way I can eliminate t/(t+f)?

I tried this:

FullSimplify[K, TransformationFunctions -> {(# /. t/(t + f) -> p &), Automatic}]


But it did not work.

• Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! Jan 27 '16 at 3:38

Eliminate[{
k == (a b c t)/(Sqrt[(f + t)^2]),
p == t/(t + f)
},
{t, f}]

a^2 b^2 c^2 p^2 == k^2

k = (a b c t)/(Sqrt[(f + t)^2]);


Assuming that {t > 0, p > 0}

Simplify[k /. t + f -> t/p, {t > 0, p > 0}]

(*  a b c p  *)


Or,

Simplify[k /. f -> t (1 - p)/p, {t > 0, p > 0}]

(*  a b c p  *)


Or, assuming {0 <= p < 1, f > 0}

Simplify[k /. t -> f p/(1 - p), {0 <= p < 1, f > 0}]

(*  a b c p  *)