Every textbook i ever read makes the statement a/c + b/c = a+b/c for how one adds fractions with common denominator.

How is this math??!

The books make a statement and, sure, i can use it to solve problems and the answers are right, at what point in a study of math (i.e. high school, undergrad, post-grad) does on ACTUALLY get a proof for this? Or actually get taught how to prove this and other statements in textbooks which i'm supposed to believe based on faith with no proof. I want to understand math. How is it understanding when you just get told "this is true, use it" by every textbook.

I want to understand math and truly believe it is true i.e. PROOF--the whole point of math. Is it some kind of joke where students are told "Math is about reason and makes sense and you don't need faith" yet one is never shown how to arrive at the conclusion a/c + b/c = a+b/c, for example, and is just told it is true.

If you ask most high school teachers why do you invert and multiple when dividing by a fraction.. they cannot tell you (with proof).

At what point in being a math student will a textbook actually hand over the goods? Can someone point me to a place i can actually learn this. (Im basically at pre-calculus level of math)

In other words, what subject in math gives me these answers i am seeking.. i.e. the proof for a/c + b/c = a+b/c? And everything else i've been taught as being "true" in math textbooks from age of 13-17. Sure, it gives true answers. But where the heck is the proof and the understanding part going to enter my math education so that i can say... "THIS is why.... a/b / c/d = a*d / b * c"