# What does the word rational in rational fraction refer to

I understand that a rational fraction is an element in the fraction field $F(X)$ and that a fraction $f$ is represented by a quotient of two poloynomials $A\over B$ under the relation ${A\over B}={C\over D}\leftrightarrow AD=BC$, but what I don't understand is the word rational in this context what does it refer to ? why not simply say a fraction , or more preciseley a fraction of polynomials ? what's the meaning of rational here especially when the field $F$ is not the field $\mathbb Q$ of rationals !! thank you for your help !

This probably has some deeper historical reasons behind it. But in any case, we need to be able to make a distinction between a fraction over $F$: $$\frac{a}{b}, \qquad a,b,\in F,$$ and a rational fraction over $F$: $$\frac{p(X)}{q(X)},$$ where $p,q$ are polynomials in $X$ with coefficients in the field $F$. If you also call the latter a fraction (which it is, but not over $F$), there is a possibility for confusion. And although fraction of polynomials would be appropriate, it is longer (and that's where the historical reasons probably kick in).