# Evaluating the limit $\lim_{x\to-1}\frac{\sqrt{x}-1}{x-1}$

How would you solve $\displaystyle\lim_{x\rightarrow-1}\left(\dfrac{\sqrt{x}-1}{x-1}\right)$ ?

I tried multiplying it by the conjugate. I don't know how to get rid of the square root.

• I tried multiplying it by the conjugate. I don't know how to get rid of the square root. – Audrey Nov 11 '14 at 10:07
• You can't, it is out of the domain. – Yves Daoust Nov 11 '14 at 10:07
• Are you sure that's $x \rightarrow -1$ and not $x \rightarrow 1^{-}$? – daOnlyBG Nov 11 '14 at 10:12
• Yup, this is the question. I'm sure. – Audrey Nov 11 '14 at 10:15
• Unless your course deals with complex numbers, $x\to-1$ is a typo for $x\to 1$. Assuming that it's a typo, you can use Autolatry' s hint. – Brian M. Scott Nov 11 '14 at 10:23

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