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