Rationalize \(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\)
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Correct Answer: Option A
Explanation:
\(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\)
= \((\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}})(\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}})\)
= \(\frac{2\sqrt{15} + 6 + 5 + \sqrt{15}}{5 - 3}\)
= \(\frac{3\sqrt{15} + 11}{2}\)
\(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\)
= \((\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}})(\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}})\)
= \(\frac{2\sqrt{15} + 6 + 5 + \sqrt{15}}{5 - 3}\)
= \(\frac{3\sqrt{15} + 11}{2}\)