Simplify Surds Expression

🎥 Video Solution:


📘 Simplify:

\[ \frac{1}{2+\sqrt{3}} + \frac{2}{\sqrt{5}-\sqrt{3}} + \frac{1}{2-\sqrt{5}} \]

✏️ Solution (Rationalisation Flow):

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

\[ = \frac{2-\sqrt{3}}{4-3} + \frac{2(\sqrt{5}+\sqrt{3})}{5-3} + \frac{2+\sqrt{5}}{4-5} \]

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

\[ = 0 \]

✅ Final Answer: \(0\)

Next Question / Full Exercise

Spread the love

Leave a Comment

Your email address will not be published. Required fields are marked *