🎥 Video Solution:
📘 Simplify:
\[ \frac{2}{\sqrt{5}+\sqrt{3}} + \frac{1}{\sqrt{3}+\sqrt{2}} + \frac{3}{\sqrt{5}+\sqrt{2}} \]
✏️ Solution (Rationalisation Flow):
\[ = \frac{2(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})} + \frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})} + \frac{3(\sqrt{5}-\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})} \]
\[ = \frac{2(\sqrt{5}-\sqrt{3})}{5-3} + \frac{\sqrt{3}-\sqrt{2}}{3-2} + \frac{3(\sqrt{5}-\sqrt{2})}{5-2} \]
\[ = (\sqrt{5}-\sqrt{3}) + (\sqrt{3}-\sqrt{2}) + (\sqrt{5}-\sqrt{2}) \]
\[ = 2\sqrt{5} – 2\sqrt{2} \]
✅ Final Answer: \(2(\sqrt{5} – \sqrt{2})\)