If A, B and $$(adj (A^{-1})+adj(B^{-1}))$$ are non-singular matrices of same order, then the inverse of $$A(adj(A^{-1}+adj(B^{-1}))^{-1}B$$, is equal to

A

$$AB^{-1}+A^{-1}B$$

B

$$adj(B^{-1})+adj(A^{-1})$$

C

$$\frac{AB^{-1}}{|A|}+\frac{BA^{-1}}{|B|}$$

D

$$\frac{1}{|AB|}(adj(B)+adj(A))$$