I'm currently studying for my upcoming precalculus midterm, but I'm having troubles rationalizing denominators and simplifying--and I'm not sure if I'm approaching this correctly. If anyone could lend me pointers to simplify please let me know, I'm really weak in this area.

Use a sum or difference formula to find the exact value of the given expression:

I figured...

Thus according to the values...

I totally got the wrong answer from here. How should I go about simplifying this?