Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)
A
5 - 2\(\sqrt{6}\)
B
5 + 2\(\sqrt{6}\)
C
5\(\sqrt{6}\)
D
5
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)
= \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) x \(\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}}\)
\(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)}\)
\(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12}\)
= \(\frac{30 + 12\sqrt{6}}{6}\)
= 5 + 2\(\sqrt{6}\)
Source: Myschool Past Questions Archive (Record #31382)