# How do I divide an implicitly defined functions?

I have two pretty ugly functions $y$, defined in open form (closed form expressions are not possible).

Where $v_1=x$, these functions look quite simple:

Now I want to divide the first function by the second (the red by the black). How do I do this? I know that to divide the first function by some constant $c$, I need to multiply the $y$ in the first expression by $c$. However, since the multiplicand is not a constant, but another open-form function, I'm not sure how to proceed.

By the way, I'm using Desmos.com for the functions.

• I like this question. But I am confused by one thing: what do you mean by "divide [these two] functions? Usually $f/g$ is the function which, when evaluated at $x$, outputs $f(x)/g(x)$. But in general an implicitly defined curve is not a function; in particular $f(x)$ might not be defined or (worse) it might not have a unique value. This causes some problem with the usual definition of division... [Think $x^2+y^2=1$ for a simple example. ] – aleph_two Oct 21 '18 at 5:25