The question:

Determine f/g, and give the domain.

$\displaystyle f(x) = \sqrt{x -1}$

$\displaystyle g(x) = x - \sqrt{x + 1}$

I did:

$\displaystyle \frac{\sqrt{x-1}}{x - \sqrt{x + 1}}$

And I found that x had to be >= 1 (since you can't square root a negative value). I wrote [1, inf) as my answer. However, the answer is $\displaystyle [1, \frac{1 + \sqrt{5}}{2}) U (\frac{1 + \sqrt{5}}{2}, \inf)$

I'm not sure how this answer was calculated. Any assistance would be awesome. Thanks.