Question

simplify 7 + √3 / 7 - √3 + 7 - √3 / 7 +√3

Answer 1

(7+√3)/(7-√3) + (7-√3)/(7+√3)    [rationalizing it]
=(7+√3)/(7-√3) ×(7+√3)/(7+√3)  + (7-√3)/(7+√3) ×(7-√3)/(7-√3) 
=(7 +√3)²/(49-3) + (7-√3)²/(49-3)
=(49 +3+ 14√3 +49+3 -14√3)/46
= 104/46 = 52/23

Answer 2

7+root3/7-root3+7-root/7+root3

=7-root3+7+root3 (+root3/7 and -root3/7 gets cancelled)

=7+7 (-root3 and +root gets cancelled)

=14.