Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
A
\(-5 - 2\sqrt{6}\)
B
\(-5 + 3\sqrt{2}\)
C
\(5 - 2\sqrt{3}\)
D
\(5 + 2\sqrt{6}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
= \((\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}})(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}})\)
= \(\frac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}\)
= \(\frac{5 + 2\sqrt{6}}{-1}\)
= \(- 5 - 2\sqrt{6}\)
Source: Myschool Past Questions Archive (Record #54951)