A 'rational function' can be written as...

(1)

... where and are polynomial in x of degree n and m so that we can write...

(2)

... or equivalently...

(3)

At the end of nineteenth century it has been demonstrated that is...

(4)

... or equivalently...

(5)

Combining (3) and (5) we find that is...

(6)

... so that the situation described by NCA is impossible...

Kind regards