Rationalise the denominator of the following : `(1)/(sqrt(3)-sqrt(2)-1`'

Answer

N/a

Explanation

(i) `(1)/(sqrt(3)-sqrt(2)-1)=(1)/((sqrt(3)-sqrt(2))-1)xx(sqrt(3)-sqrt(2)+1)/((sqrt(3)-sqrt(2))+1)`
[to find the conjugate write first terms insides the bracket i.e., treating first two terms as one term and then change the sign between this new term and third term]
`=(sqrt(3)-sqrt(2)+1)/((sqrt(3)-sqrt(2))^(2)-1)" "[because(a-b)(a+b)=a^(2)-b^(2)]`
`(sqrt(3)-sqrt(2)+1)/(3+2-2sqrt(6)-1)=(sqrt(3)-sqrt(2)+1)/(4-2sqrt(6))=(sqrt(3)-sqrt(2)+1)/(2(2-sqrt(6)))xx(2+sqrt(6))/(2+sqrt(6))`
`=(2sqrt(3)-2sqrt(2)+2+sqrt(18)-sqrt(12)+sqrt(6))/(2(4-6))=(2sqrt(3)-2sqrt(2)+2+3sqrt(2)-2+3sqrt(2)-2sqrt(3)+sqrt(6))/(-4)`
`=-(1)/(4)(sqrt(2)+sqrt(6)+2)`