If
![a_i \ (i = 1, 2, \ldots, n)](/media/m/9/d/5/9d5de624506ded54c221d79f1a0b6dc2.png)
are distinct non-zero real numbers, prove that the equation
![\frac{a_1}{a_1-x} + \frac{a_2}{a_2-x}+\cdots+\frac{a_n}{a_n-x} = n](/media/m/1/1/9/119afb98a160d437d31a6a379aa419a7.png)
has at least
![n - 1](/media/m/b/9/f/b9f2e24ffd917df5f63d30599dd3220c.png)
real roots.
%V0
If $a_i \ (i = 1, 2, \ldots, n)$ are distinct non-zero real numbers, prove that the equation
$$\frac{a_1}{a_1-x} + \frac{a_2}{a_2-x}+\cdots+\frac{a_n}{a_n-x} = n$$
has at least $n - 1$ real roots.