MathDB

There is an equation

\sum_{i=1}^{n}{\frac{b_i}{x-a_i}}=c

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

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