Expert: Sherman D. - 2/23/2004

Question
[(Square root of 3 divided by 3) plus 1]/ [1- (square root of 3 divided by 3)]

Answer
if by this mean

[((sqrt(3))/3) + 1] / [1 - ((sqrt(3))/3)]

same as

[((sqrt(3))/3) + 1] / [-((sqrt(3))/3) + 1]

Multiply top and bottom by 3

[((sqrt(3) + 3)/3] / [(-(sqrt(3) + 3)/3]

Multiply top half by reciprocal of bottom half and you get

[3((sqrt(3) + 3))]/[3(-sqrt(3) + 3)]

the 3s cancel out, which leaves you with

[sqrt(3) + 3]/[-sqrt(3) + 3]

becomes

[3 + sqrt(3)]/[3 - sqrt(3)]

Multiply top and bottom by 3 + sqrt(3)

[(3 + sqrt(3))*(3 + sqrt(3))]/[(3 - sqrt(3))*(3 + sqrt(3))]

[9 + 3sqrt(3) + 3sqrt(3) + (sqrt(3))^2] /
[9 + 3sqrt(3) - 3sqrt(3) - (sqrt(3))^2]

[9 + 6sqrt(3) + 3]/[9 - 3]

becomes

[12 + 6sqrt(3)]/6

[6(2 + sqrt(3))]/6

the 6s cancel out

the answer is

2 + sqrt(3)

I have worked this out on a calculator, and i got your problem and my answer to be the same thing.