jmc

Let $n$ be a positive integer greater than or equal to $3$. Let $a,b$ be integers such that $ab$ is invertible modulo $n$ and $(ab{)}^{-1}\equiv 2(\mathrm{mod}n)$. Given $a+b$ is invertible, what is the remainder when $(a+b{)}^{-1}(a^{-1}+b^{-1})$ is divided by $n$?