And I think your random tests are so much wrong. I cannot put screenshots here, so I'll push the text with Console.logs(). My previous code version did the calculations correctly, but your tests showed issue when:

frac1 = -32783 / -87302
frac2 = -70901 / 96443

They expect "377758809/631610602" (positive).
My correct output is "-377758809/631610602" (negative).

Similarly another example:

-53524/-96771
-76017/4842

Test Failed
Assert.That(Kata.divideFractions(randomFrac1, randomFrac2), Is.EqualTo(expected))
Expected string length 20 but was 21. Strings differ at index 0.
Expected: "259163208/1233693485"
But was: "-259163208/1233693485"

Wtf are these tests?

"The fractions will never be improper."

Meanwhile your tests:

55013/-84661

13455/71078 :)

or

-91877/-61523

82703/79988

Since when deonomiator having "-" sign is a valid fraction? XD

Have you actually tried testing that claim? I've tested 5 solutions (mine, the linq solution commented on, yours and two others from this comment thread). Only one commenter I tested in this thread (zokeer) has a solution that actually runs faster than the Linq solutions (though at least all the solutions run in linear time against varying string lengths and varying unique character amounts). Both yours and Zub_Son's are slower than the Linq solutions despite commenting on the alleged slowness of it.

Not only are the Linq solutions easier to write and read, this shows that most people trying to make faster/more optimized solutions end up slower than the naive Linq one. Add in that such optimizations aren't really necessary unless the method is an a hot path and I'll prefer a competently written short Linq solution 90% of the time.

Regex as best practices? Who da hell upvotes this solution?

Who gives this piece of a bad code "best practices"? He could also name every variable a/b/c/d/e/f....

I did the solution with over 40 lines of code and time complexity was still O(N log (n) ), so looking at this solution is embarrasing

tbh yeah TC is O(nLog(n)) and SC is O(n) when it can be done with nested loops with TC of O(n^2) and SC of O(1) but seems like less code

WHO DA HELL VOTES FOR THE BEST PRACTICES? It's soooooooo SLOW!

Who press the "Best Practices" button? This solution is slower than turtle....

raise it to a positive(?) exponent

I think it is a bit more complex than that.

Things are even better! By e^iπ = -1, you can have a positive number, raise it to a positive(?) exponent, and get a negative result! How cool is that!

Well, kinda. All it takes is some... imagination.

See solutions
Crying out of misery

Literally everyone of us, with some kata, at some point of time

After 2 hours of trying to figure it out myself
Giving up and came here to search help
I notice wikipedia article - Complex Numbers
Quickly reading contents trying to make sense of it all
I dig deeper into imaginary unit article
After hour I understand what's going on
After 30 minutes the code is ready
Runs without any problems and I submit
See solutions
Crying out of misery

Check this: https://en.wikipedia.org/wiki/Complex_number