What is the conjugate of  `3/(1 + sqrt 3)` ? Show work

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`3/(1+sqrt3)`

To get the conjugate of the above expression, express it in the form a +b, first.

To do so, rationalize the denominator. So, multiply the top and bottom by the conjugate of the denominator.

To get the conjugate of the denominator 1 + sqrt3, change the operation between the two terms to its opposite. So, the conjugate of 1+sqrt3 is 1-sqrt3.

`3/(1+sqrt3)`

`=3/(1+sqrt3)*(1-sqrt3)/(1-sqrt3)`

`=(3-3sqrt3)/(1-3)`

`=(3-3sqrt3)/(-2)`

`=-3/2+(3sqrt3)/2`

`=(3sqrt3)/2-3/2`

Now that the given expression is in the form a+b, to get its conjugate change the operation between terms to its opposite.

Hence, the conjugate of   `3/(1+sqrt3)`   is  `(3sqrt3)+3/2` .

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