`((1+sqrt(2))/(sqrt(5)+sqrt(3))+(1-sqrt(2))/(sqrt(5)-sqrt(3)))` का सरलीकरण है

Options

A. `sqrt(5)+sqrt(6)`
B. `2sqrt(5)+sqrt(6)`
C. `sqrt(5)-sqrt(6)`
D. `2sqrt(5)-3sqrt(6)`

Answer

C

Explanation

`((1+sqrt(2))/(sqrt(5)+sqrt(3))+(1-sqrt(2))/(sqrt(5)-sqrt(3)))`
`implies ((1+sqrt(2))(sqrt(5)-sqrt(3))+(1-sqrt(2))(sqrt(5)+sqrt(3)))/((sqrt(5)+sqrt(3))(sqrt(5)-sqrt(3)))`
`implies (sqrt(5)-sqrt(3)+sqrt(10)-sqrt(6)+sqrt(5)+sqrt(3)-sqrt(10)-sqrt(6))/((sqrt(5))^(2)-(sqrt(3))^(2))`
`implies (2sqrt(5)-2sqrt(6))/2implies(2(sqrt(5)-sqrt(6)))/2`
`implies (sqrt(5)-sqrt(6))`