Express each one of the following with rational denominator: `(3sqrt(2)+\ 1)/(2sqrt(5)-3)` (ii) `(b^2)/(sqrt(a^2+b^2)+\ a)`

Explanation

`(i) (3sqrt(2)+ 1)/(2sqrt(5)-3)`
Rationalising factor for `1/(2sqrt5-3)` is `2sqrt5 -3`
`(3sqrt2+1)/(2sqrt5-3)`
`(3sqrt2+1)/(2sqrt5-3)xx(2sqrt5+3)/(2sqrt5+3)`
`((3sqrt2+1)(2sqrt5+3))/((2sqrt5-3)(2sqrt5+3))`
`(3sqrt2xx2sqrt5+3sqrt2xx3+1xx2sqrt5+1xx3)/((2sqrt5)^2-(3)^2)`
`(6sqrt10+9sqrt2+2sqrt5+3)/(20-9)`
`(6sqrt10+9sqrt2+2sqrt5+3)/11`
`(ii) (b^2)/(sqrt(a^2+b^2)+a)`
`(b^2)/(sqrt(a^2+b^2)+a)xx(sqrt(a^2+b^2)-a)/(sqrt(a^2+b^2)-a)`
`(b^2(sqrta^2+b^2)-a)/((sqrta^2+b^2)^2-(a)^2)`
`(b^2(sqrta^2+b^2)-a)/(a^2+b^2-a^2)`
`(b^2(sqrta^2+b^2)-a)/(b^2)`
`(sqrta^2+b^2)-a)`