Simplify (frac{2sqrt{2} – sqrt{3}}{sqrt{2} + sqrt{3}})
-
A.
3(sqrt{6} – 7) -
B.
3(sqrt{6} + 7) -
C.
3(sqrt{6} – 1) -
D.
3(sqrt{6} + 1)
Correct Answer: Option A
Explanation
(= frac{2sqrt{2} – sqrt{3}}{sqrt{2} + sqrt{3}} times frac{sqrt{2} – sqrt{3}}{sqrt{2} – sqrt{3}})
(= frac{2sqrt{2}(sqrt{2}) + (2sqrt{2})(-sqrt{3})-sqrt{3}(sqrt{2})-sqrt{3}(-sqrt{3})}{(sqrt{2})^2-(sqrt{3})^2})
(= frac{2 times 2 – 2sqrt{6} – sqrt{6} + 3}{2 – 3})
(= frac{4 – 3sqrt{6} + 3}{-1})
(= frac{7 – 3sqrt{6}}{-1})
(= frac{7}{-1} – frac{3sqrt{6}}{-1})
(= -7 + 3sqrt{6})
(= 3sqrt{6}-7)
There is an explanation video available below.