lim h->0 (((1/(1+h))-1)/h

Question

I don't understand how the answer is -1 shouldn't it be 0?

Answer 1

Just look at the part
1/(1+h) - 1
= 1/(1+h) - 1/1
using a common denominator of 1+h
we get
(1 - 1+h)/(1+h)
= -h/(1+h)
so lim h->0 (((1/(1+h))-1)/h
= lim(-h/(1+h))/h
doesn't the h cancel?
so now we have
Lim -1(1+h) as h -->0
= -1/(1+0)
= -1

Answer 2

Got it, thanks :)