Question

multiply the denominators (1+√5)(1-√5)

Answer 1

the conjugates and simplify ???

Answer 2

??? Denominators? Conjugates?
\[(1+\sqrt{5})(1-\sqrt{5}) = -4\]

Answer 3

Actually, (1+square root 5) and (1-square root 5) are conjugates of each other. Since you mention denominators, do you mean the problem should be as follows:
(1+square root 5)/(1-square root 5)? If so, then the following solution can be arrived at:

[(1+square root 5)/(1-square root 5)]*[(1+square root 5)/(1+square root 5)]
[1+2(square root 5)+5]/(1-5)=[6+2(square root 5]/-4

Therefore, the answer is: -(3+square root 5)/2