If (√5-1)/(√5+1)-(√5+1)/(√5-1) = a + b√5, then the value of (a + b) (a - b) ÷ a² + b² is:

Correct option is C

Solution:

​$$\frac{\sqrt{5} - 1}{\sqrt{5} + 1} - \frac{\sqrt{5} + 1}{\sqrt{5} - 1}$$ =a +b$$\sqrt5$$​

$$\frac{(\sqrt{5} - 1)(\sqrt{5} - 1)}{(\sqrt{5} + 1)(\sqrt{5} - 1)} - \frac{(\sqrt{5} +1)(\sqrt{5} +1)}{(\sqrt{5} + 1)(\sqrt{5} - 1)}$$ =a +b$$\sqrt5$$​​

$$\frac{6-2\sqrt5}{4}$$ -$$\frac{6+2\sqrt5}{4}$$=a +b$$\sqrt5$$ 

o -$$\sqrt5$$ =a +b$$\sqrt5$$​

a=0 , b=-1 

so, value 

(a + b) (a - b) ÷ a² + b² 

put a=0 , b=-1 

(0 + (-1)) (0 - (-1)) ÷ (0)² + (-1)²

=  (-1)(1)

=-1 
​