I have experimental data points that can be modeled by two different rational polynomials.
I am wondering if there is a way (e.g. by a transform or integral), to discriminate the following two rational polynomials (defined for $x\in\mathcal{R}^+$):
$$f_1(x)=\frac{a+bx^2}{c+dx^2}$$
and
$$f_2(x)=\frac{d+ex^2+fx^4}{g+hx^2+lx^4}$$
where $a,b,c,d,e,f,g,h,l>0$.
Any suggestion?