Get mathematica to simplify expression with another equation

Question

I have a very complicated mathematica expression that I\'d like to simplify by using a new, possibly dimensionless parameter.

An example of my expression is:

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Answer 1

Have you tried this?

K = a*b*t/((t + f) c*d);
Solve[p == t/(t + f), t]
 -> {{t -> -((f p)/(-1 + p))}}

Simplify[K /. %[[1]] ]
 -> (a b p)/(c d)

EDIT: Oh, and are you aware of Eliminiate?

Eliminate[{eq1, eq2}, {t,f}]
 -> a b p == c d K && c != 0 && d != 0

Solve[%, K]
 -> {{K -> (a b p)/(c d)}}

EDIT 2: Also, in this simple case, solving for K and t simultaneously seems to do the trick, too:

Solve[{eq1, eq2}, {K, t}]
 -> {{K -> (a b p)/(c d), t -> -((f p)/(-1 + p))}}