Given two distributions $F_1(x)$ and $F_2(x)$.
I know that the following two expectations are equal. $$ \int_x \frac{a}{c-x}dF_1(x) = \int_x \frac{b}{c-x}dF_2(x) = C>0 $$
And I know that $a>b>0$. Can I conclude that $F_1$ and $F_2$ satisfy that one FOSD the other? If not, how can I find a counter-example?
Thanks a lot!