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Question
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Solution
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
= `(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)) xx (sqrt(7) - sqrt(5))/(sqrt(7) - sqrt(5)`
= `(sqrt(7) - sqrt(5))^2/((sqrt(7))^2 - (sqrt(5))^2`
= `(7 + 5 - 2sqrt(35))/(7 - 5)`
= `(12 - 2sqrt(35))/(2)`
= 6 - `sqrt(35)`
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