How can I tell if a tensor equation has a non-trivial solution or no solution at all?

Question

I have the equation $C^{ab}A_{ab}=X^{ab}(A_{ab}+B_{ab})$. Is there a non-trivial solution to solve for the tensor $X^{ab}$ where none of the tensors can be set to zero? How would I solve for it?

If I say $D_{ab}:=(A_{ab}+B_{ab})$ is invertible then I can solve for $X^{ab}$. How can I solve for $X^{ab}$ if $D_{ab}$ or its constituents are not invertible?