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Question
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
Solution
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
= `((sqrt(5) + sqrt(3))^2 + (sqrt(5) - sqrt(3))^2)/((sqrt(5) - sqrt(3))(sqrt(5) + sqrt(3))`
= `(5 + 3 + sqrt(15) + 5 + 3 - sqrt(15))/(5 - 3)`
= `(16)/(2)`
= 8
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