I'm working through some rationalization problems and came across this problem:

$\frac{\left(\frac{1}{\sqrt{x}}\right)-1}{x-1}$

The answer is given as:

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

I can't for the life of me figure out how to get there. Pretty sure I'm supposed to multiply $\frac{1}{\sqrt{x}}-1$ by its conjugate radical $\frac{1}{\sqrt{x}}+1$, but I still can't get to their answer.

A step-by-step rationalization would be much appreciated!