Question

As x goes to zero, what is the limit of (( 1/ x+2) -(1/2)) / x?
I know the answer is -1/4, but I'm confused on how to get that answer. I think I have to multiply by the reciprocal.

Answer 1

1/(x+2) - 1/2
= (2-(x+2)) / 2(x+2)
= -x/(2(x+2))

Now divide that by x, and you are left with

-1/(2(x+2)) -> -1/4

You can divide by x, because until you take the limit, x is not zero.