simplifying expressions - Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes.

My current method is to put the combination over a single denominator with Together[], then look at the CoefficientArrays[] of the numerator and make sure all entries vanish. The trouble is, the step using Together[] is very time consuming, and seems in some cases to get stuck (basically, the process just runs the CPU with a fixed memory usage for hours, when normally Together has a pattern of rising and falling memory usage as it shrinks the expression it creates).

My assumption is that the problem with using Together in this context is that it doesn't just put everything over a single denominator, it also tries to factor out common terms. But I don't need it to factor out common terms, since a failure to factor something will just mean a few more redundant equations to solve. Is there anything like Together, that doesn't bother with trying to cancel things? Or an option to make Together give up after a certain (reasonable) amount of time?

Edit: To those suggesting just multiplying through by the product of the denominators, one issue is that not all of the objects are expressed as P/Q. So for example, say I have:

(1/(1-v)-v/(1-w))/((1-v)(1-u)) - (1-w)/(u v w(1-v))

I want this expressed as one object, P/Q, and I don't care about canceling common factors between P and Q. Is there a function that does that? I suppose I could just repeatedly multiply through by all denominators for each subexpression, but that seems inefficient.

Comments

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I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

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