8. Liu Shang and Luo In $\triangle A B C$, take a point $D, E, F$ on the three sides $A B, B C, C A$ respectively, such that $\frac{A D}{D B}=\frac{B E}{E C}=\frac{C F}{F A}=r>0$. Then the ratio of the area of $\triangle D E F$ to the area of $\triangle A B C$ is . $\qquad$
8. $\frac{1+2 r-2 r^{2}}{1+2 r+r^{2}}$