KöMaL 2017 B4860

Assume that $a<b<c<d$ and $a+d\ne b+c$. Show that the equation $\frac1{a-x}-\frac1{b-x}-\frac{1}{c-x}+\frac1{d-x}=0$ has exactly two distinct roots, such that one of them lies in the interval $(b,c)$, and the other one lies outside the interval $(a,d)$.