If `(sqrt(3)-1)/(sqrt(3)+1)=x+ysqrt(3)` , find the value of `x\ a n d\ y`

Explanation

`(sqrt(3)-1)/(sqrt(3)+1)=((sqrt(3)-1)\(sqrt(3)-1))/((sqrt(3)+1)\(sqrt(3)-1))`
Rationalising the denominator
`=(sqrt(3)-1)^2/((sqrt3)^2-(1)^2)`
`=(3+1-2sqrt3)/(3-1)`
`=(4-2sqrt3)/2`
`=2-sqrt3`
Therefore,
`2-sqrt3=x+ysqrt3`
Comparing, we get
`x=2 and y=-1`