Total Length of the Solution Set

Let $f(x) = \dfrac{1}{x-a} + \dfrac{1}{x-b}$ with $a, b \in \mathbb{R}$.

1. If $a = b = 1$, solve the inequality $f(x) > 1$. 2. Define the length of each of the intervals $(m, n)$, $[m, n)$, $(m, n]$, $[m, n]$ to be $n - m$. If $a < b$, find the length (or, if the solution set is a union of intervals, the total length) of the solution set of $f(x) > 1$.