Zero/Zero questions and perhaps faulty logic
So I only have an Algebra II level understanding of math seeing as I am still in high school and am still missing some fundamentals seeing as I didn't pay attention in math until this year. However when recalling something my algebra teacher had taught me during the year I came up with some questions regarding the logic recently.
So during the school year, I was taught that and so forth but ... and while researching this topic I found that the algebraic way to write all these fractions is as such and upon researching this further I found that the reason that is undefined is that for any value of the equation holds true. However, seeing as in the fraction is a variable and variables can represent any given quantity I was wondering in the case that would still and if not why along with the fact that lets say and you didn't know it why is it safe to assume that would never equal zero? Also if it happens to be the case where when (which I doubt it is) shouldn't this mean that then?