$D$ and $E$ are points on the sides $AB$ and $AC$ of triangle $ABC$, and $DE$ is parallel to $BC$. If $DB=\frac{3}{7}AB$, then $\frac{AE}{EC}$ equals ____.

If $DB$ is $\frac{3}{7}$ of $AB$, then $AD=AB-DB=\frac{4}{7}$ of $AB$. Hence $\frac{AD}{DB}=\frac{4/7}{3/7}=\frac{4}{3}$, and BPT transfers this to $\frac{AE}{EC}=\frac{4}{3}$. The option $\frac{3}{4}$ is the correct ratio inverted; $\frac{3}{7}$ merely copies the given fraction; $\frac{4}{7}$ is $\frac{AD}{AB}$, a part-to-whole ratio where a part-to-part ratio was asked for.