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      Question

      Simplify: (√5 + √2)/(√5 − √2) + (√5

      − √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 − b) + (a − b)/(a + b) Combine: = [(a + b)² + (a − b)²] / (a² − b²) = [a² + 2ab + b² + a² − 2ab + b²] / (a² − b²) = [2a² + 2b²] / (a² − b²) = 2(a² + b²)/(a² − b²) Now a² = 5, b² = 2: ⇒ 2(5 + 2)/(5 − 2) = 2×7 / 3 = 14/3

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