Hey there, I'm just trying to work out how to find the largest possible domain to the following function algebraically.

$\displaystyle f(x)=\sqrt{\frac{x-1}{x+2}}$

The way I've been going about it is:

$\displaystyle x-1$ must be greater than zero, so $\displaystyle x\geq1$

$\displaystyle x+2$ must be greater than zero, so $\displaystyle x\geq-2$

and $\displaystyle \sqrt{x+2}$ can't equal zero, meaning, for this part, $\displaystyle x$ can be any real number besides $\displaystyle -2$

From this I get the domain of $\displaystyle \left [1,\infty\right )$

Which is not the complete domain stated in the answer. I must be missing something...

Thanks for your help