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(3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+...

`(3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(sqrt(12))/(sqrt(3)-sqrt(2))`

Text Solution

Verified by Experts

We have given `(3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(sqrt(12))/(sqrt(3)-sqrt(2))`
Now we can rationalize both the terms.
`=> (3sqrt2-2sqrt3)/(3sqrt2+2sqrt3)*(3sqrt2-2sqrt3)/(3sqrt2-2sqrt3)+sqrt12/(sqrt3-sqrt2)*(sqrt3+sqrt2)/(sqrt3+sqrt2)`
`= (18+12-12sqrt6)/(18-12)+(2sqrt3(sqrt3+sqrt2))/(3-2)`
`= (30-12sqrt6)/6+(6+2sqrt6)/1`
`= 5-2sqrt6+6+2sqrt6`
`= 11`.
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