There's no need to be so rude. The OP was just asking why the negative value is distributed over the entire fraction when it doesn't have brackets.
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 would rather be rude than not to understand the mathematics.
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...