If (frac{(2sqrt{3}-sqrt{2})}{(sqrt{3}+2sqrt{2})} = m +nsqrt{6}), find the values of m and n respectively.

**A.**

1, -2**B.**

-2, 1**C.**

(frac{-2}{5}), 1**D.**

2, 3/5

##### Correct Answer: Option B

##### Explanation

Rationalize (frac{(2sqrt{3}-sqrt{2})}{(sqrt{3}+2sqrt{2})}) and equate to (m +nsqrt{6}). Such that m = -2, and n = 1.

Use (sqrt{3}-2sqrt{2}) as the conjugate for Rationalization

(frac{(2sqrt{3}-sqrt{2})}{(sqrt{3}+2sqrt{2})}) X (frac{(sqrt{3}-2sqrt{2})}{(sqrt{3}-2sqrt{2})})

(frac{6 – 4sqrt{6} – sqrt{6} + 4}{3 – 2sqrt{6} + 2sqrt{6} – 8})

=(frac{10 – 5sqrt{6}}{-5})

= -2 + (sqrt{6})