Hail Stewart-2!

Geometry Level 2

Let ABCDABCD be a square, and let EE and FF be points on ABAB and BC,BC, respectively. The line through EE parallel to BCBC and the line through FF parallel to ABAB divide ABCDABCD into two squares and two non-square rectangles. The sum of the areas of the two squares is 910\frac{9}{10} of the area of square ABCD.ABCD.

Find AEEB+EBAE.\frac{AE}{EB}+\frac{EB}{AE}.

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