$\lim_{x\to1}\frac{x + \sqrt{x}}{\sqrt{x-1}}$ $\lim_{x\to1}\frac{x - \sqrt{x}}{\sqrt{x-1}}$
Lately I've been trying to satisfy some curiosity about the nature of limits and I found this example, it's really bugging me that I can't solve it. It seems so simple, yet when I attempt to solve it, it's like I'm trapped in a loop. Everything I do, undos the previous action.
I'll take anything you can give, a solution, a good hint... I tried manipulating the expression without changing it, but I can't get through it.