I'm having a bit of a difficult time understanding a problem that asks:

Find all values of $\displaystyle {a}$ such that

$\displaystyle \lim_{x\to1}\left(\frac{1}{x-1}-\frac{a}{x^2-1}\right)$

exists and is finite.

I feel that this should be simple, but I am stuck. The following is about as far I can make sense of it:

$\displaystyle \rightarrow \lim_{x\to1}\left(\frac{1}{x-1}-\frac{a}{(x-1)(x+1)}\right)$

$\displaystyle \rightarrow \lim_{x\to1}\left(\frac{x+1}{(x-1)(x+1)}-\frac{a}{(x-1)(x+1)}\right)$

$\displaystyle \rightarrow \lim_{x\to1}\left(\frac{x+1-a}{(x-1)(x+1)}\right)$

Thinking about numbers very close to 1, I believe a = 2; however, I am unable to work through it.

Any help in understanding what I am not seeing would be greatly appreciated.

Thank you in advance.

Take care.

/alan