Question

What is the limit of `( 1/(x-1) - 2/(x^2-1) )` as x approaches 1?

Answer 1

Have a look:

Answer 2

`lim_(xrarr1)(1/(x-1)-2/(x^2-1)) = lim_(xrarr1)((x+1)-2)/((x+1)(x-1))`

`= lim_(xrarr1)(x-1)/((x+1)(x-1)) = lim_(xrarr1) 1/(x+1) = 1/2`