I have the following original expression:
(100 c)/(e y) + (100 b x)/(e y) + (100 a x^2)/(e y) == 0
which, after factoring out the common terms looks like this intermediate expression:
(100 (c + b x + a x^2))/(e y) == 0
100/(e y) is a common factor, and all of the variables are assumed to be positive numbers, I can cancel it out to obtain the target expression, ready for solving:
c + b x + a x^2 == 0
In summary, I need to be able to "cancel out" all common factors for any kind of algebraic expression, such as in the above example.
Numerator[Factor[(100 a)/(e y) + (100 b x)/(e y) + (100 c x^2)/(e y)]]
100 (a + b x + c x^2) == 0, which does not satisfy the goal of obtaining an expression without common factors.