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