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If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = ...

If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), 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 is B

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

 

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

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

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

=\(\frac{10 - 5\sqrt{6}}{-5}\)

= -2 + \(\sqrt{6}\)