Lim [(1/x-/x^2-1)], x-> 1 right answer is 1/2

As you've probably noticed by now, both fractions' denominators turn out to be 0 when x = 1, so direct substitution is no good right now. However, we can combine the fractions first:



Notice now that we can safely cancel out the x - 1 term because, since this is a limit, we only care about what happens near 1 instead of at 1, and the fraction is defined near 1. Doing so gives the fraction , and substituting in 1 for x gives the answer .