Evaluating: $ \lim\limits_{x\to 1^{-}}\left[\ln\left(1-x \over 1 + x\right) - \ln\left(1 - x^{2}\right)\right] $ I would like to evaluate the following limit:
$$
\lim_{x\to 1^{-}}\left[%
\ln\left(1-x \over 1 + x\right) - \ln\left(1 - x^{2}\right)\right]
$$
I put this into a limit calculator and the calculator gave as answer $-\log\left(4\right)$. Why ?.
Should the answer not be?:
$$
\lim_{x \to 1^{-}}\ln\left(1 - x \over 1+x\right)
-\lim_{x \to 1^{-}}\ln\left(1 - x^{2}\right)
=-\infty - \left(-\infty\right) = -\infty + \infty$$
My second, and to me more important question, what is the value of $$-\infty + \infty$$
Thanks for your help.

Your expression $-\infty + \infty$ is an indeterminate form, much like $\frac{0}{0}$ or $\frac{\infty}{\infty}$. So, on its own, it has no meaning.
In your specific case, using the property of logs that $\ln(AB) = \ln(A) + \ln(B)$ will likely be helpful here.
