[Math] Limit of a function with square roots

Question

I've got the following limit to solve:

$$\lim_{s\to 1} \frac{\sqrt{s}-s^2}{1-\sqrt{s}}$$

I was taught to multiply by the conjugate to get rid of roots, but that doesn't help, or at least I don't know what to do once I do it. I can't find a way to make the denominator not be zero when replacing $s$ for $1$. Help?

Answer 1

Try putting $t=\sqrt s$ to get $$\frac {t-t^4}{1-t}=\frac {t(1-t^3)}{1-t}=t(1+t+t^2)$$You can notice this without the substitution, of course, but sometimes a substitution like this helps to clarify what is going on.