How do you get the result of this limit?

[itsrayex]

The result is 1/2 but I can't reach the same solution. Can you tell me what I did wrong and how to reach the correct solution? thank you

 

[blamocur]

You've made a mistake in the first expression of the second line.

 

[Deleted member 4993]

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

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

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

= \(\displaystyle \frac{x-1}{(x - 1)*(x+1)}\)

= \(\displaystyle \frac{1}{x+1}\) ..........................continue