HMMT 2004 U19

The Fibonacci numbers are defined by $F_{1}=F_{2}=1$, and $F_{n}=F_{n-1}+F_{n-2}$ for $n \geq 3$. If the number

$$\frac{F_{2003}}{F_{2002}}-\frac{F_{2004}}{F_{2003}}$$

is written as a fraction in lowest terms, what is the numerator?