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Question
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
Solution
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
= `((sqrt(7) - sqrt(3))^2 - (sqrt(7) + sqrt(3))^2)/((sqrt(7) + sqrt(3))(sqrt(7) - sqrt(3))`
= `(7 + 3 - 2sqrt(21) - 7 - 3 - 2sqrt(21))/((sqrt(7))^2 - (sqrt(3))^2`
= `(-4sqrt(21))/(7 - 3)`
= `-sqrt(21)`
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