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Question
Simplify the following
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
Solution
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
= `((4 + sqrt(5))^2 + (4 - sqrt(5))^2)/((4 - sqrt(5))(4 + sqrt(5))`
= `(16 + 5 + 8sqrt(5) + 16 + 5 - 8sqrt(5))/(16 - 5)`
= `(42)/(11)`
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