Mathematica: Putting an expression in terms of a specific variable

[camron_m21]

My problem is this: I have an algebraic expression, and I want to express it in terms of one variable divided by another. It's a fairly large expression, and I'd like to do it in mathematica before attempting it by hand. I've tried Simplify, FullSimplify and Solve, but none of these have done the trick. Here is the expression:

$$\alpha = \frac{L}{(1+I_2)} \left(1 - \frac{I_2 \epsilon \gamma_a}{2 \gamma} \frac{((\gamma_a \gamma'' - \Delta^2)(2 \gamma^2 + \Delta^2) - \Delta^2 (\gamma_a + \gamma) \gamma))}{((\gamma_a \gamma'' - \Delta^2)^2 + \Delta^2 (\gamma_a + \gamma)^2}\right)$$

Where $$L = \frac{\gamma^2}{\gamma^2 + \Delta^2} , \gamma_a = q \gamma$$ , and $$\gamma'' = \gamma (1 + I_2)$$.

And I want to solve this as a function of $$\frac{\Delta}{\gamma}$$. Does anyone know how to do this in Mathematica?

 

[Simon_Tyler]

Essentially you just need to use the replacement rule
\[CapitalDelta] -> \[Gamma] \[Delta]
then solve for \[Delta].

Provided I typed in your equation properly (not all of the parentheses matched up), the result is a messy cubic in \[Delta]^2.

See the attached Mma file.