HELP with Simplifying this expression! (Intro to Pre-Calc)?

Question

http://i539.photobucket.com/albums/ff355/annienguyena/EE.png

the problem is in the image because it's just alot easier that way.

Answer 1

Let s = ( 1 + sqrt(2) ) / (3 - sqrt(2) ).

Multiply top and bottom by 3 + sqrt(2).

That makes the bottom the difference of two squares, and eliminates the surds.

s = [ (1 + sqrt(2))(3 + sqrt(2)) ] / [ (3 + sqrt(2))(3 - sqrt(2)) ]

= [ 3 + 4 sqrt(2) + 2 ] / [ 9 - 2 ]

= ( 5 + 4 sqrt(2) ) / 7.