I have:
$F(x) + G(x) = 1 + F(x)*M,$
$G(x) = T_{1}(x) + T_{2}(x) + ... + T_{N}(x)$
$F(x )x^{a_{i}} = T_{i}(x) \times C_{i}(x) + \sum_{j \leq N} T_{j}(x) \times P_{ji}(x)$
In which $M, N, a_{i}, C_{i}(x), P_{ji}(x)$ are known consts or polynomials. How can I represent $F(x)$ or $G(x)$ in form of these known factors?
UPDATE: Degree of $C_{i}, P_{ji}$ are smaller than $a_{i}$
Thank you,