(2x)/(2x) =/= 2x/2x

The parenthesis have meaning here. 2x/2x does not have parenthesis, there is no "assumed" parenthesis.

Please look at the evidence that lead to that conclusion

http://www.wolframalpha.com/input/?i=2x%C3%B72x

Implied multiplication takes precedence over multiplication and division.

x = (x/1)^1

This is implied.

2x is as simple as we can make the term without knowing the value of x

(2x/1)^1 is implied.

48/x is as simple as you can make this term without knowing the value of x.

48/xb is as simple as you can make this term without knowing the value of x or b.

[(48/xb)/1]^1 is implied.

48/xb != 48 ÷ x * b

Multiplication and division are same level functions:

10/5 ÷ 10/5 = 1

If you arrive at something different you have made an error. This is not disputable.

2x/2x = 1

48/ab = 48/(ab)

http://www.wolframalpha.com/input/?i=48%2Fa%28b%29

implied multiplication = implied parenthesis.

2x4y6z/2x4y6z = 1

Anything else is a comprehension issue. Following OoO for the sake of OoO is dumb.

Please point to examples for which following OoO to the letter doesn't result in serious issues in every other related problem.

Dude this is not true and you have yet to give any evidence to the contrary.

Implied operators only take precedence for the purpose of ease of user input in single line fields in regards to programming. It is not solid mathematics, nor is it accurate. It is merely for convenience purposes, because most people will enter 2x/2x meaning (2x)/(2x).