Question 6
(HUN 1) 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.
$$\frac{a_1}{a_1-x}+\frac{a_2}{a_2-x}+\cdots+\frac{a_n}{a_n-x}=n$$
has at least $n-1$ real roots.