# Math Help - Limit of Quotients help

1. ## Limit of Quotients help

I've just started my semester of Calculus and I find limits relatively easy except for these type of questions. Any help would be appreactied, I just need to see it worked out and then I would understand it.

Lim 1/x-1 + 1/x+1 DIVIDED BY x
x-0

I got to:

lim 1/x-1 + 1/x+1
x-0
DIVIDED BY
lim x
x-0

but I dont know what to do after.

Thanks!

2. If the requested limit is...

$\displaystyle \lim_{x \rightarrow 0} \frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}$ (1)

... then the most confortable way is to use the elementary algebra...

$\displaystyle \frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}= \frac{\frac{x+1+x-1}{x^{2}-1}}{x}= \frac{\frac{2x}{x^{2}-1}}{x}= \frac{2}{x^{2}-1}$ (2)

May be that the requested limit is different from (1)... in any case the Latex is very useful to avoid misundestanding ...

Kind regards

$\chi$ $\sigma$

3. I guess this what your question is,

[tex]\lim_{x\rightarrow 0}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x} [\tex]

if so, simplify and get the following, and rest will be much easy

$lim_{x\rightarrow 0} \frac{2}{x^2-1}$