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SSC CHSL 12 Nov 2025 Shift 2 Paper

Question : 70 of 100

Marks: +1, -0

Simplify:

\frac{1}{\sqrt{5}-2}+\frac{1}{\sqrt{5}+2}

Solution:

Concept:

Use the identity

(a-b)(a+b)=a^2-b^2

to combine fractions by rationalizing the denominators.

Explanation:

Step 1: Write the sum with a common denominator:

(\sqrt{5}-2)(\sqrt{5}+2)

Step 2: Numerator becomes

(\sqrt{5}+2) + (\sqrt{5}-2) = 2\sqrt{5}

Step 3: Denominator simplifies to

(\sqrt{5})^2 - (2)^2 = 5 - 4 = 1

Step 4: Therefore, the expression equals

2\sqrt{5} / 1 = 2\sqrt{5}

Answer:

Option A:

2\sqrt{5}

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