Explanation of an equation

Question

Given a system $AX=B$ and a perturbed system $(A+E)Y=B+F$ with $E$ and $F$ being the perturbation matrices, how does the following second equation come? Consider $A$ and $(A+E)$ both to be invertible.

$$X-Y=A^{-1}B-(A+E)^{-1}(B+F)=(A+E)^{-1}(EX-F)$$

Answer 1

It's \begin{align}(A+E)(A^{-1}B-(A+E)^{-1}(B+F))&=(A+E)A^{-1}B-B-F\\&=B+EA^{-1}B-B-F\\&=B+EA^{-1}B-B-F\\&=EX-F\end{align}