imc

Let $x=BD$ and $y=CD$. Therefore, $AB=4x$ and $AC=9y$, as shown in the diagram(the labels on the bottom are for that line segment while the labels on the top are from one point to the left to one point to the right). From this, we can see that $AD=10y=5x$, and since $BC=BD-CD=x-y$. Now, our ratio is $\frac{x-y}{AD}$. We can split this into 2 fractions: $\frac{x}{AD}-\frac{y}{AD}=\frac{x}{5x}-\frac{y}{10y}=\frac{1}{5}-\frac{1}{10}=\boxed{\frac{1}{10}}$