Originally Posted by

**capandbells** Hi. I have this problem on my homework:

$\displaystyle

\lim_{x \to 1} \frac{1}{ln(x)}-\frac{1}{x-1}

$

I know it's the indeterminate form $\displaystyle \infty - \infty$. I've tried using l'Hopital's Rule, but it doesn't seem to help. (It just becomes $\displaystyle \lim_{x \to 1} - \frac{1}{xln(x)^2} - \frac{1}{(x-1)^2}$ which isn't any better.)

I've also tried combining the fractions and taking the derivative, which is extraordinarily tedious and also doesn't help. I know by graphing that the limit is supposed to be 1/2, but I can't figure out a way to make that work. Is there something I'm missing? I haven't been this bothered by a math problem in a long time. Any help you can offer would be greatly appreciated. Thanks!