OK guys I got it!

The answer is four.

First we equate

cos C = CD/(x+1) and cos C = [ (x+1)^2 + x^2 - (x-1)^2 ] / [2(x+1)(x)]

to find an expression for CD in terms of x then

cos A = AD/(x-1) and cos A = [ (x-1)^2 + x^2 - (x+1)^2 ] / [2(x-1)(x)]

to find an expression for DA in terms of x. Then subtracting CD-DA gives 4.