Which one of the following is NOT a valid conclusion when DE is parallel to BC in triangle ABC, with D on AB and E on AC?

BPT itself gives $\frac{AD}{DB}=\frac{AE}{EC}$; adding 1 to both sides of the reciprocal form gives $\frac{AB}{DB}=\frac{AC}{EC}$; and the similarity of triangles $ADE$ and $ABC$ gives $\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}$. Note carefully that $DE:BC$ matches $AD:AB$, the part-to-WHOLE ratio, so $\frac{AD}{DB}=\frac{DE}{BC}$ is false in general — for $AD=4,DB=6$ it would claim $\frac{DE}{BC}=\frac{2}{3}$ when the true value is $\frac{2}{5}$.