Question 200667
Nope.
Make it easy on yourself, forget the polynomials and try the problem using integers. Take an instance and see if it works, If it won;t work for numbers, it wont work for polynomials

So, let's take 20/6
result 3 1/3

Now take 20/3
result 6 2/3

1/3 <> 2/3 so you can see they are not equal. If there is a speficic case where the proposal fails to hold, then it cannot hold in general

So in one easy step you found a case where the proposed answer fails. All it takes is one !