If a = (√ 5 + 1) / (√ 5 - 1) and b = (√ 5 - 1) / ( √ 5 + 1) then the value of (a 2 + ab + b 2) / (a 2 - ab + b 2) is?

a = [(√5 + 1) / (√5-1)] x [(√5 + 1) / (√5 + 1)]
= (√5 + 1)² / (5 - 1)
= (5 + 1 + 2 √5) / 4
= (3 + √5) / 2
b = [(√5 - 1) / (√5 + 1)] x [(√5 - 1 ) / (√5 -1)]
= (√5 - 1 )² / (5 - 1)
= (5 + 1 - 2√5) / 4
= (3 - √5) / 2
Now a² + b² = [(3 + √5)² + (3 - √5)²] / 4
= [2 x (9 + 5 )] / 4
= 7
ab = 1
∴ (a² + ab + b²) / (a² - ab + b²)
= (7 + 1) / (7 - 1)
= 8/6
= 4 / 3