Remember that in similar triangles the corresponding sides are proportional. Knowing this, we can establish a proportion between sides AD and AB, and between sides ED and CB.
[tex] \frac{AD}{AB} = \frac{ED}{CB} [/tex]
[tex]\frac{AD}{2} = \frac{1}{x}[/tex]
Notice that AD=2+1=3, so:
[tex] \frac{3}{2} = \frac{1}{x} [/tex]
Solving for [tex]x[/tex]:
[tex]x= \frac{2}{3} [/tex]
We can conclude that the value of [tex]x[/tex] is [tex] \frac{2}{3} [/tex]
