SMO 2007 Junior Round 1 Question 20

Suppose that $a+x^2=2006$, $b+x^2=2007$ and $c+x^2=2008$ and $abc=3$. Find the value of
$$\frac a{bc}+\frac b{ca}+\frac c{ab}-\frac1a-\frac1b-\frac1c.$$