Question
Simplify: (√5 + √3)/(√5 − √3) + (√5
− √3)/(√5 + √3)Solution
Let a = √5, b = √3. 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) Now a² = 5, b² = 3: = 2(5 + 3)/(5 − 3) = 2×8/2 = 8.
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