It will be "something else".
The question is whether you can rationalize the division of two polynomials to create a polynomial. The answer to that is No, not generally.
Consider for example,
fplot(@x) x ./ (x + 1), [-5 5])
This has a discontinuity at x = -1, being positive to the left and negative to the right, with asymptotic 0 at either side. This is clearly not a polynomial.