problem: Find the value of the expression. $$\frac{7+8+9}{2+3+4}\cdot\frac{6+9+12}{9+8+7}$$
solution: Notice that there is a $7+8+9$ in the numerator and a $9+8+7$ in the denominator. Cancel these, leaving $\frac{6+9+12}{2+3+4}$. At this point, simply perform the addition to get $\frac{27}{9}$, which equals $\boxed{3}$.