1. The problem statement, all variables and given/known data Okay, so if f and g are continuous functions at a, then prove that f/g is continuous at a if and only if g(a) # 0 2. Relevant equations Assuming to start off the g(a)#0, by the delta-epsilon definition of continuity, basically, We know that |f(x)| and |g(x)| are bounded. 3. The attempt at a solution I have messed around with the end result that we need, which is when |x-a|< delta |f(x)/g(x)-f(a)g(a)|<Epsilon. This is what I've come up with: |1/(g(x)g(a))|*|f(x)g(a)-f(a)g(x)|. By looking at each piece it seems like they can be bounded as well. However, how do i manipulate what each one is bounded by so that when I multiply and add everything out, I get a nice simple Epsilon?