Is the $\left|\frac{f(x)}{g(x)}\right|$ always equivalent to $\frac{\left|f(x)\right|}{\left|g(x)\right|}$

Question

Can I split the modulus of a rational function into two parts like this

$$ \left|\frac{f(x)}{g(x)}\right|=\frac{\left|f(x)\right|}{\left|g(x)\right|} \ $$

Is this statement always true for any function (or at least for polynomials)

Thanks