((1/2+h) -(1/2)) / h

found LCD of numerator
((2)-(2+h)/2(2+h))/h
is it 1

I think you have a typo and you meant:

((1/(2+h)) -(1/2)) / h
if so:
= ( (2 - 2 - h)/(2(h+2)) / h
= -h/(2(h+2))/h
= -1/(2h+4)