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Simplify 1/(sqrt(5)+sqrt(6)-sqrt(11))...

Simplify `1/(sqrt(5)+sqrt(6)-sqrt(11))`

Text Solution

Verified by Experts

`1/(sqrt5+sqrt6-sqrt11) = 1/(sqrt5+sqrt6-sqrt11)**((sqrt5+sqrt6)+sqrt11)/((sqrt5+sqrt6)+sqrt11)`
`= ((sqrt5+sqrt6)+sqrt11)/(((sqrt5+sqrt6)^2-sqrt11^2))`
`=(sqrt5+sqrt6+sqrt11)/(5+6+2sqrt30 -11)`
`=(sqrt5+sqrt6+sqrt11)/(2sqrt30)`, which is the required solution.
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