Partial fractions expansion via polynomial equations

A new method is suggested for solving the polynomial equation
A(s)X(s)+B(s)Y(s)=C(s)
where
A (s), B (s), C (s)
are given polynomials and
X (s), Y (s)
are to be determined. The method is then used for the formulation of the partial-fraction expansion of transfer functions, and for computing the greatest common divisor of polynomials