Why does $αA^{−1} + (1 −α)B^{−1}\succeq (αA + (1 − α)B)^{−1}$

Question

Let $A, B \in M_n$ be positive definite and let $α\in (0, 1)$. Why does $αA^{−1} + (1 −α)B^{−1}\succeq (αA + (1 − α)B)^{−1}$?