Simplify Surds Expression

🎥 Video Solution:


📘 Simplify:

\[ \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} + \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}} \]

✏️ Solution:

\[ = \frac{(\sqrt{5}+\sqrt{3})^2 + (\sqrt{5}-\sqrt{3})^2}{5 – 3} \]

\[ = \frac{(5+3+2\sqrt{15}) + (5+3-2\sqrt{15})}{2} \]

\[ = \frac{16}{2} \]

\[ = 8 \]

✅ Final Answer: \(8\)

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