AoPS Wiki:Problem of the Day/September 9, 2011

Assume that $a$ , $b$ , and $c$ are roots of $2x^3-2x^2-x+4.$ Let $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}$ be equal to $-p/q$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .