Different video cards for different software?

reading some review article I dug up. I found the Firepro cards work very well with OpenGL, GTX cards work very well with DirectX, and Radeon cards work very well with OpenCL. So it seems like you have situation were, one may want 3 different kinds of video cards depending on the task: a GTX, Firepro, and a Radeon.

three different computers, each dedicated to one of those API’s.

Or one big machine with the three different cards in them. So I don’t know: I am unfamiliar with such a configuration, would the cards fight with each other for dominance? Also most motherboards do not support full 16x on PCIe slots. I’m not sure, maybe someone can tell me, but that would mean one would only be getting full bandwidth on the first card, Unless one gets an expensive $300.00 motherboard that supports, x16/x16/x16.

http://www.tomshardware.com/reviews/radeon-r9-290-review-benchmark,3659-12.html

Don’t conflate “Works best with” with meaning “Sucks for all the others”.
Each card works best with what it was designed to do and less as effectively with the other tasks.
For example, the embedded Intel HD chip is great at saving laptop battery power but sucks for Windows OpenGL and is only OK for DirectX.
It’s all a compromise.
My current personal favorite that isn’t expensive and does a good job of everything is the Nvidia GeForce GT 750.

Thanks for the Info