Basically, we treat the fraction as an entire quantity, so when you are subtracting a fraction, you are subtracting ALL terms in the fraction. This is why you need to distribute the negative across all terms in the fraction.
I don't mind if people from the upper-levels of a subject are rude (i.e. my maths professor who responds with "Oh, that's easy" to every question asked towards him and ignores the student entirely; though I don't expect much better academic quality from a community college) but I think it's just counter-productive when a student is willing to learn on his/her own and the only response to that is "go learn on your own" without pointing them towards a specific textbook and maybe even which books/resources to avoid (as to prevent the student from learning the material incorrectly, as I find many websites practice the spread of disinformation).
Well Daigo, we've been exposed to "math teachers" too; there's a couple I would have loved to shoot!
But you seem like a reasonable student; you do "see" WHY it's difficult to teach "some stuff" from a
"type it out" site like this (like, no blackboard and stuff...); agree???
You showed in post#6 some weird work(!). I'll try to show the "how" (I'll use a and b !) :
2b - a + b = 2b + b - a = 3b - a
2b - (a + b) = 2b - a - b = 2b - b - a = b - a
2b - (a - b) = 2b - a + b = 3b - a (same as the 1st one)
Make sure you "follow" that before going to something more involved...