MathNet 1992 — Part 01 Question 46

Let $f(x) = \dfrac{a_{1}}{x + a_{1}} + \dfrac{a_{2}}{x + a_{2}} + \ldots + \dfrac{a_{n}}{x + a_{n}}$, where $a_{i}$ are unequal positive reals. Find the sum of the lengths of the intervals in which $f(x) \geq 1$.