hello:

i wonder if this has been answered. it's been posted a while back, i'm new to wyzant, and i don't see an answer yet. so, since i'm here, let's try this:

i believe the problem may be written this way:

lim { (1/h) *{ [ 1/(x+h)] - [1/x] } }      as h→0

combining denominators:

lim { (1/h) *{ [ (x) - (x+h) ] / [ (x) * (x+h) ] } }     as h→0

the x's on the numerator cancels and you're left with (-h) in the numerator, which yields:

lim { (1/h) *{ [ -h ] / [ (x) * (x+h) ] } }      as h→0

the h in the numerator and the h in the denominator of the left-most term, i.e. (1/h) cancel, which yields:

lim {  [-1] / [ (x) * (x+h) ] }      as h→0

as h→0, the denominator becomes [ x^2 ]; thus the answer is:

[(-1) / (x^2)].

Feel free to submit any equation you need help with