How to find the roots of a sum of divisions of polynomials

How can I find those x values in which this function becomes f(x)=0?

I have 4 vectors of length N: A, B, C, D, and

f(x) = sum( ( x*A_i - B_i ) / ((x*C_i - D_i)^3) )

Answer 1

[Torsten]

Multiply by

prod (x*C_i - D_i)^3

and determine the roots of the resulting polynomial of degree 3*(N-1)+1 using the "roots" command.

You might want to use symbolic computations in advance using expand, collect, and subst to get the numerical coefficients of this polynomial.

[Nieves Lopez]

Thank you for your help