Woah what a ratio!!

$\triangle ABC$ is an acute-angled triangle with $AB=13$ , $BC=14$ and $AC=15$ . the circle $\Gamma$ with centre $I$ touches $BC$ at $D$ . Let $AI$ produced meet $BC$ at $E$ . Find the numerical value of $\dfrac{[ABC]}{[ AID]-[IDE]}$

$[PQRS]$ means area of the figure $PQRS$