Simplify (frac{1}{1 + sqrt{5}}) – (frac{1}{1 – sqrt{5}})
-
A.
– (frac{1}{2}sqrt{5}) -
B.
(frac{1}{2}sqrt{5}) -
C.
– (frac{1}{4}sqrt{5}) -
D.
5
Correct Answer: Option B
Explanation
(frac{1}{1 + sqrt{5}}) – (frac{1}{1 – sqrt{5}})
= (frac{1 – sqrt{5} – 1 – sqrt{5}}{(1 + sqrt{5}) (1 – sqrt{5}})
= (frac{-2sqrt{5}}{1 – 5})
= (frac{-2sqrt{5}}{- 4})
= (frac{1}{2}sqrt{5})