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Question
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
Solution
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
= `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)) xx (3sqrt(5) + 2sqrt(6))/(3sqrt(5) + 2sqrt(6)`
= `(6sqrt(30) + 24 - 15 - 2sqrt(30))/((3sqrt(5))^2 - (2sqrt(6))^2`
= `(6sqrt(30) + 9 - 2sqrt(30))/(45 - 24)`
= `(4sqrt(30) + 9)/(21)`
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