Discussion

Question:

The expression 1 - $\frac{1}{1 + \sqrt{3}}$ + $\frac{1}{1 - \sqrt{3}}$ equals:

Explanation:

1 - $\frac{1}{1 + \sqrt{3}}$ + $\frac{1}{1 - \sqrt{3}}$

Taking LCM of denominators, we get

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

= $\frac{1 - 3 - 1 + \sqrt{3} + 1 + \sqrt{3}}{1 - 3}$

= $\frac{- 2 + 2 \sqrt{3}}{- 2}$

= $1 - \sqrt{3}$

Hence, option (a).

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