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