Math Help - limit of 1/(x-1)

1. limit of 1/(x-1)

Hi, is it possible to evaluate 1/(x-1) at x=1 by any means?

Thanks

2. As x gets closer and closer to 1, the numerator remains 1 while the denominator gets closer and closer to 0- the entire fraction (in absolute value) gets larger and larger- there is NO limit.

You can't even say " $\displaytype\lim_{x\to 1}\frac{1}{x- 1}= \infty$".

If x< 1, the denominator is negative so $\displaytype\lim_{x\to 1^-}\frac{1}{x- 1}= -\infty$.

If x> 1, the denominator is positive so $\displaytype\lim_{x\to 1^+}\frac{1}{x- 1}= \infty$.