2002 #11 and 31

I love algebra!

Difficulty: moderately difficult for students, but I enjoyed the heck out of it. Guaranteed that they will forget about (x+2) at the end.

Difficulty: There are many possible subsets, so this didn't thrill me at first and I didn't notice the shortcut.  When I read it, it was obvious.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for  example. Source: UVM Math Contest

answer 11 and answer 31.