Contribution of a term in a fraction I have a value 
$$v=\frac{A_2+B_2+C_2}{A_1+B_1+C_1}.$$ 
I want to estimate the contribution of $A_2/A_1$ to $v$. 
I know it is not possible to mathematically derive $A_2/A_1$ out of $v$. 
My question is if there is any approximation method for the contribution. 
And if there is, what kind of assumption the method has for the approximation. 
With kind advice from @fcop, @Nick Cox, @whuber, let me clarify further. 
What's given is an example and in actuality, 
(1). A1, A2, B1, B2,... are variables. 
(2). there are an undefined number of variables in the formula. 
(3). subscript after terms represents a status, where there is only two status (1 and 2). 
When $v$ represent a collective property change between status 1 and 2, what I want to know is the contribution of each variable to the change. 
As for the assumption for the approximation, I was expecting something like if values of all variables are in the same scale, then $$\frac{A_2}{A_1} = v\times \frac{B_1+C_1}{B_2+C_2}$$, so to speak. 
I am sorry for the confusion, I should have given more thoughts before asking. 
 A: The answer to this question depends heavily on the type of data you are collecting, the nature of the errors in the measured relationship, and a variety of other consideration. However, I will direct you to the example of Michaelis Menten equations in biochemistry. It is a somewhat wellknown example of nonlinear regression, where a variety of terms combine in ratios to contribute to an outcome.
You have not exactly written a statistical model.
Now I am assuming that the parameters in your model arise from some form of 5 variable dataset, for example of the following format
v   x_1 w_1 x_2 w_2
0     2   7   7   3
1     3   5   8   1

And the actual modeled association is:
$$E[v|X_1, W_1, X_2, W_2] = \frac{A_1 + B_1 x_1 + C_1 w_1}{A_2 + B_2 x_2 + C_2 w_2}$$
So, in trying to address the question: What is the expected difference in $v$ comparing groups that differ by 1 unit in $X_1 / X_2$, controlling for $W_1$ and $W_2$ you can address that from the estimated model and coefficients using the $\delta$-method.
A: You can conceive of the individual ratios as slopes of lines through the origin, and (conditioning on the status-1 values) the combined ratio (or mediant) as a weighted average slope.
Let $r_A = A_2/A_1$ and so on. Then
$v=\frac{A_2+B_2+C_2}{A_1+B_1+C_1} = \frac{A_1\,r_A +B_1\,r_B+C_1\,r_C }{A_1+B_1+C_1}$
So seeing the status-1 values as weights, that's a weighted average of the ratios.

For example, if the subscript $1$ (initial status) represented some initial exposure, you could call it an exposure-weighted average of the individual slopes.
If all the values are positive, we can see various things as a result; for example, the value of the mediant must lie between the largest and the smallest individual ratios.
