Answer
The mistake is that $\sqrt 3 \times \sqrt 3$ is $\sqrt 9$. The square root of 9 is 3 not 9 because 3 x 3 = 9
The correct answer is $\frac{\sqrt 3 - 1}{2}$
Work Step by Step
$\frac{1}{\sqrt 3 -1}$
We multiply the faraction by the conjugate of $\sqrt 3 -1$ which is $\sqrt 3 +1$
$\frac{1}{\sqrt 3 -1} \times \frac{\sqrt 3 +1}{\sqrt 3 +1}$
We multiply the numerator by the numerator and the denominator by the denominator.
$\frac{1 \times \sqrt 3 +1}{\sqrt 3 -1 \times \sqrt 3 +1}$
$\frac{\sqrt 3 - 1}{\sqrt 9 - 1}$
Square root of 9 is 3 because 3 x 3 = 9
$\frac{\sqrt 3 - 1}{3 - 1}$
$\frac{\sqrt 3 - 1}{2}$
The mistake is that $\sqrt 3 \times \sqrt 3$ is $\sqrt 9$. The square root of 9 is 3 not 9 because 3 x 3 = 9
