$$\left( {\frac{{1 + \sqrt 2 }}{{\sqrt 5 + \sqrt 3 }} + \frac{{1 - \sqrt 2 }}{{\sqrt 5 - \sqrt 3 }}} \right)$$ simplifies to = ?
A. $$\sqrt 5 + \sqrt 6 $$
B. $${\text{2}}\sqrt 5 + \sqrt 6 $$
C. $$\sqrt 5 - \sqrt 6 $$
D. $${\text{2}}\sqrt 5 - 3\sqrt 6 $$
Answer: Option C
Solution(By Examveda Team)
$$\frac{{1 + \sqrt 2 }}{{\sqrt 5 + \sqrt 3 }} + \frac{{1 - \sqrt 2 }}{{\sqrt 5 - \sqrt 3 }}$$$$ \Rightarrow \frac{{\left( {1 + \sqrt 2 } \right)\left( {\sqrt 5 - \sqrt 3 } \right) + \left( {1 - \sqrt 2 } \right)\left( {\sqrt 5 + \sqrt 3 } \right)}}{{\left( {\sqrt 5 + \sqrt 3 } \right)\left( {\sqrt 5 - \sqrt 3 } \right)}}$$
$$ \Rightarrow \frac{{\sqrt 5 - \sqrt 3 + \sqrt {10} - \sqrt 6 + \sqrt 5 + \sqrt 3 - \sqrt {10} - \sqrt 6 }}{{5 - 3}}$$
$$\eqalign{ & \Rightarrow \frac{{2\sqrt 5 - 2\sqrt 6 }}{2} \cr & \Rightarrow \frac{{2\left( {\sqrt 5 - \sqrt 6 } \right)}}{2} \cr & \Rightarrow \sqrt 5 - \sqrt 6 \cr} $$
This Question Belongs to Arithmetic Ability >> Surds And Indices
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