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Question
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Solution
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
= `(3(5 + sqrt(3)) + 2(5 - sqrt(3)))/((5 - sqrt(3))(5 + sqrt(3))`
= `(15 + 3sqrt(3) + 10 - 2sqrt(3))/((5)^2 - (sqrt(3))^2`
= `(25 + sqrt(3))/(25 - 3)`
= `(25 + sqrt(3))/(22)`
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