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    Question

    Simplify: (√5 + √2)/(√5 βˆ’ √2) + (√5

    βˆ’ √2)/(√5 + √2)
    A 17/5 Correct Answer Incorrect Answer
    B 14/3 Correct Answer Incorrect Answer
    C 21/5 Correct Answer Incorrect Answer
    D 11/5 Correct Answer Incorrect Answer

    Solution

    Let a = √5, b = √2. Expression = (a + b)/(a βˆ’ b) + (a βˆ’ b)/(a + b) Combine: = [(a + b)Β² + (a βˆ’ b)Β²] / (aΒ² βˆ’ bΒ²) = [aΒ² + 2ab + bΒ² + aΒ² βˆ’ 2ab + bΒ²] / (aΒ² βˆ’ bΒ²) = [2aΒ² + 2bΒ²] / (aΒ² βˆ’ bΒ²) = 2(aΒ² + bΒ²)/(aΒ² βˆ’ bΒ²) Now aΒ² = 5, bΒ² = 2: β‡’ 2(5 + 2)/(5 βˆ’ 2) = 2Γ—7 / 3 = 14/3

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