Question

√5+1/√5-1+√5-1/√5+1

Please solve with reason...

Answer 1

Multiply and divide by (√5-1)(√5+1)

((√5+1)(√5+1) + (√5-1)(√5-1) ) / ((√5-1)(√5+1))

The denominator is of the form (a-b)(a+b)=a^2-b^2
a=√5
a^2 = 5
b=1
b^2 = 1
a^2-b^2 = 4

The left side is:
((√5+1)^2 +(√5-1)^2 ) /4
= ((5+2√5+1) + (5-2√5+1) ) /4
= (5+1+5+1)/4
= 12/4
= 3