Question
Simplify the expression: (√7 + √5)/(√7 −
√5) + (√7 − √5)/(√7 + √5)Solution
Let a = √7, b = √5. 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 = 7, b² = 5: = 2(7 + 5)/(7 − 5) = 2×12 / 2 = 12.
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