निम्नलिखित प्रत्येक को सरल कीजिए :
(i) `(5+sqrt(6))/(5-sqrt(6))` , (ii) `(7-3sqrt(5))/(7+3sqrt(5))`

Explanation

(i) `(5+sqrt(6))/(5-sqrt(6)) = (5+sqrt(6))/(5-sqrt(6)) xx (5+sqrt(6))/(5+sqrt(6))`
`= ((5)^(2) + (sqrt(6))^(2) + 2(5)(sqrt(6)))/((5)^(2) - (sqrt(6))^(2)) = (25 + 6 + 10sqrt(6))/(25- 6 ) = (31+ 10sqrt(6))/(19)`
(ii) `(7-3sqrt(5))/(7+3sqrt(5)) = (7-3sqrt(5))/(7+3sqrt(5)) xx (7-3sqrt(5))/(7-3sqrt(5)) = ((7)^(2) + (3sqrt(5))^(2) - 2(7) (3sqrt(5)))/((7)^(2) - (3sqrt(5))^(2))`
`= (49 + 45 + 42sqrt(5))/(49 - 45) = (94 - 42 sqrt(5))/(4) = (47- 21sqrt(15))/(2)`