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

Options

A. `2-sqrt(3)`
B. `2+sqrt(3)`
C. `16-sqrt(3)`
D. `40-sqrt(3)`

Answer

C

Explanation

`((2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)-1)/(sqrt(3)+1))`
`(((2+sqrt(3))^(2)+(2-sqrt(3))^(2))/((2-sqrt(3))(2+sqrt(3)))+(sqrt(3)-1)/(sqrt(3)+1)xx(sqrt(3)-1)/(sqrt(3)-1))`
`implies((4+3+4sqrt(3)+4+3-4sqrt(3))/(4-3)+((sqrt(3)-1)^(2))/(3-1))`
`implies (14+(3+1-2sqrt(3))/2)`
`implies14+(2(2-sqrt(3)))/2`
`implies14+2-sqrt(3)=16-sqrt(3)`