IT-CESENATICO 2012 Problem 1

On the sides of a triangle $ABC$ right angled at $A$ three points $D, E$ and $F$ (respectively $BC, AC$ and $AB$ ) are chosen so that the quadrilateral $AFDE$ is a square. If $x$ is the length of the side of the square, show that $$\frac{1}{x}=\frac{1}{AB}+\frac{1}{AC}$$