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    Question

    Simplify: (√3 + 1)/(√3 − 1) + (√3 −

    1)/(√3 + 1)
    A 8 Correct Answer Incorrect Answer
    B 1 Correct Answer Incorrect Answer
    C 4 Correct Answer Incorrect Answer
    D 11 Correct Answer Incorrect Answer

    Solution

    Let a = √3, b = 1. Expression = (a + b)/(a − b) + (a − b)/(a + b) = [(a + b)² + (a − b)²] / (a² − b²) (a + b)² = a² + 2ab + b² (a − b)² = a² − 2ab + b² Sum = 2a² + 2b² Denominator = a² − b² So expression = 2(a² + b²)/(a² − b²) Here a² = 3, b² = 1 = 2(3 + 1)/(3 − 1) = 2×4 / 2 = 4.

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