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.

Hint:
Remember that $\ln(A) - \ln(B) = \ln(A/B)$.  Further, $\ln(x^a) = a\ln(x)$.  Also, $1-x^2 = (1+x)(1-x)$ is helpful.
Can you solve it from here?
