Limits Continuity And Differentiability

If \(a, b\) and \(c\) are three distinct real numbers and \(\lim _\limits{x \rightarrow \infty} \frac{(b-c) x^2+(c-a) x+(a-b)}{(a-b) x^2+(b-c) x+(c-a)}=\frac{1}{2}\), then \(a+2 c=\)