Question

simplify the following

Answer 1

$\frac{3+ \sqrt{5} }{3- \sqrt{5} }$ + $\frac{3- \sqrt{5} }{3+ \sqrt{5} }$

$\frac{(3+ \sqrt{5} )^{2} + (3- \sqrt{5} )^{2} }{(3+ \sqrt{5} )(3- \sqrt{5})}$

$\frac{(3+ \sqrt{5} )^{2} + (3- \sqrt{5} )^{2} }{3^{2}- \sqrt{5}^{2} }$

$\frac{3^{2}+ \sqrt{5}^{2}}{3^{2}- \sqrt{5}^{2}}$

$\frac{9+5}{9-5}$

$\frac{14}{4}$

$\frac{7}{2}$

$3.5$

Answer 2

 (3 + √5)/ ( 3 - √5) +( 3- √5)/ (3+ √5)
= (3+√5)² + (3 -√5)²    since [ (a+b)(a-b) =(a² -b²) ]
   (3² - (√5)² )
=  2( 3² +(√5)² )         since [  (a+b)² +(a-b)² = 2(a² + b²) ]
       9- 5
= 2( 9 + 5)
          4
= 2(14) / 4
= 28/ 4
= 7