Rationalize \(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\)
A
(3 √ 15 +11) / 2
B
3 √ 15 -11
C
(3 √ 15 -11) / 2
D
3 √ 15 +11
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\)
= \((\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}})(\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}})\)
= \(\frac{2\sqrt{15} + 6 + 5 + \sqrt{15}}{5 - 3}\)
= \(\frac{3\sqrt{15} + 11}{2}\)
Source: Myschool Past Questions Archive (Record #9642)