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Question

(4+√5)/(4-√5)+(4-√5)/(4+√5)


Solution

(4 +√5)/(4 -√5)  + (4 -√5)/(4 +√5)
now dividing and multiplying the first term by (4 +√5) and second term by (4 -√5), we get,
(4 +√5)×(4 +√5)/(4 -√5)×(4 +√5) + (4 -√5)×(4 -√5)/(4 +√5)×(4 -√5)
⇒(4 +√5)²/(16 -5) +  (4 -√5)²/(16 -5)   ( applying (a² -b²) = (a+b)(a -b))
⇒(16 +5 +8√5 +16 +5 - 8√5)/11
⇒42/11

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