Dividing polynomials is relatively simple. All we have to do is look for common factors between the numerator and the denominator of the fraction. Take, for example, the expression 2xx^4y^2/4x^2y^3. The numerator and denominator of this expression have a common factor of 2x^2y^3. We're left with the fraction 2x^2/3y.
There are times where we might have to factor the fraction in order to ferret out the common factor.
x^2 - 9/x^2 + 6x + 9
(x + 3)(x - 3) / (x + 3)(x + 3)
We see that the common factor of the numerator and denominator of the fraction is x + 3. The original fraction ultimately reduces to x - 3/x + 3.