ISL 1970 Problem 6

There is an equation $\sum_{i=1}^{n}{\frac{b_i}{x-a_i}}=c$ in $x$ , where all $b_i >0$ and $\{a_i\}$ is a strictly increasing sequence. Prove that it has $n-1$ roots such that $x_{n-1}\le a_n$ , and $a_i \le x_i$ for each $i\in\mathbb{N}, 1\le i\le n-1$ .