OMK 2019 B1

Given three nonzero real numbers $a,b,c,$ such that $a>b>c$ , prove the equation has at least one real root. $$\frac{1}{x+a}+\frac{1}{x+b}+\frac{1}{x+c}-\frac{3}{x}=0$$ @below sorry, I believe I fixed it with the added constraint.