Exams › SSC CGL (Prelims) › General

Solve and simplify: $\frac{1}{\sqrt{5}-\sqrt{2}}+\frac{1}{\sqrt{5}+\sqrt{2}}$.

1. $2\sqrt{5}$
2. $\sqrt{5}/3$
3. $2\sqrt{5}/3$
4. $\sqrt{5}$

Correct answer: $2\sqrt{5}/3$

Solution

Combine the two fractions using the standard identity. With $a=\sqrt{5}$ and $b=\sqrt{2}$, the sum becomes $\frac{2\sqrt{5}}{5-2}=\frac{2\sqrt{5}}{3}$.

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