Like any other expression, functions can be subjected to operations.
Let's define two functions, $f(x)= \frac{2x+3}{3x-2}$, and $g(x)=\frac{4x}{3x-2}$.
We can for instance divide them, which takes the following form:
$
(f/g)(x)
=\frac{\frac{2x+3}{3x-2}}{\frac{4x}{3x-2}}
=\frac{2x+3}{3x-2}\cdot\frac{3x-2}{4x}
=\frac{2x+3}{4x}
$
>⚠️ The domain of the resulting function must satisfy the constraint of never allowing a denominator of $0$. **The domains of the original functions $f(x)$ and $g(x)$ also must carry into the new domain**. Using domain notation, we can combine them to write the domain of $(f/g)(x)$ like so: $D: \left\{x | x \ne 0, x \ne \frac{2}{3}\right\}$.