Rationalize (frac{2 – sqrt5}{3 – sqrt5})
-
A.
(frac{1 – sqrt5}{2}) -
B.
(frac{1 – sqrt5}{4}) -
C.
(frac{ sqrt5 – 1}{2}) -
D.
(frac{1 + sqrt5}{4})
Correct Answer: Option B
Explanation
(frac{2 – sqrt5}{3 – sqrt5}) x (frac{3 + sqrt5}{3 + sqrt5})
(frac{(2 – sqrt5)(3 + sqrt5)}{(3 – sqrt5)(3 + sqrt5)}) = (frac{6 +2sqrt5 – 3sqrt5 – sqrt25}{9 + 3sqrt5 – 3sqrt5 – sqrt25})
= (frac{6 – sqrt5 – 5}{9 – 5})
= (frac{1 – sqrt5}{4})