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How do you simplify (sqrt(3) - 1)/(1+sqrt(3))?

1 Answer

Mar 15, 2018

$2 - \sqrt{3}$ $2-sqrt(3)$

Explanation:

$\frac{\sqrt{3} - 1}{1 + \sqrt{3}}$ $(sqrt(3)-1)/(1+sqrt(3)$ = $\frac{- 1 + \sqrt{3}}{1 + \sqrt{3}}$ $(-1+sqrt(3))/(1+sqrt(3))$

= $\frac{- 1 + \sqrt{3}}{1 + \sqrt{3}} . \frac{1 - \sqrt{3}}{1 - \sqrt{3}}$ $(-1+sqrt(3))/(1+sqrt(3)). (1-sqrt(3))/(1-sqrt(3))$

= $\frac{- 1 + 2 \sqrt{3} - 3}{1 - 3}$ $(-1+2sqrt(3)-3)/(1-3)$ = $\frac{2 \sqrt{3} - 4}{- 2}$ $(2sqrt(3)-4)/(-2)$
= $2 - \sqrt{3}$ $2-sqrt(3)$

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