Sum
Rationalise the denominator and simplify `sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2)`
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Solution
`sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2) = sqrt(5)(1/(sqrt(6) + 2) - 1/(sqrt(6) - 2))`
= `sqrt(5)[(sqrt(6) - 2 - (sqrt(6) + 2))/((sqrt(6) + 2)(sqrt(6) - 2))]`
= `sqrt(5)[(sqrt(6) - 2 - sqrt(6) - 2)/((sqrt(6))^2 - 2^2)]`
= `sqrt(5)((-4)/(6 - 4))`
= `sqrt(5)((-4)/2)`
= `sqrt(5) xx -2`
= `-2 sqrt(5)`
Concept: Rationalisation of Surds
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