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Question
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Solution
`(sqrt(3) + 1)/(sqrt(3) - 1)`
= `(sqrt(3) + 1)/(sqrt(3) - 1) xx (sqrt(3) + 1)/(sqrt(3) + 1)`
= `(sqrt(3) + 1)^2/((sqrt(3))^2 - (1)^2)`
= `((sqrt(3))^2 + 2 xx sqrt(3) xx 1 + (1)^2)/(3 - 1)`
= `(3 + 2sqrt(3) + 1)/(2)`
= `(4 + 2sqrt(3))/(2)`
= 2 + `sqrt(3)`
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