Simplify ((frac{1}{sqrt{5} + sqrt{3}} – frac{1}{sqrt{5} – sqrt{3}}) times frac{1}{sqrt{3}})
-
A.
(frac{sqrt{3}}{sqrt{5}}) -
B.
(frac{2 sqrt{3}}{7}) -
C.
-2 -
D.
-1
Correct Answer: Option D
Explanation
((frac{1}{sqrt{5} + sqrt{3}} – frac{1}{sqrt{5} – sqrt{3}}) times frac{1}{sqrt{3}})
(frac{1}{sqrt{5} + sqrt{3}} – frac{1}{sqrt{5} – sqrt{3}})
(frac{(sqrt{5} – sqrt{3}) – (sqrt{5} + sqrt{3})}{(sqrt{5} + sqrt{3})(sqrt{5} – sqrt{3})})
= (frac{sqrt{5} – sqrt{3} – sqrt{5} – sqrt{3}}{5 – sqrt{15} + sqrt{15} – 3})
= (frac{-2sqrt{3}}{2})
= (- sqrt{3})
(therefore (frac{1}{sqrt{5} + sqrt{3}} – frac{1}{sqrt{5} – sqrt{3}}) times frac{1}{sqrt{3}} = – sqrt{3} times frac{1}{sqrt{3}})
= (-1)