[1/(x+h) - 1/x] / h =

Combine the terms in the numerator

(1 / (x + h) - 1 / x) =>
(x / (x * (x + h)) - (x + h) / (x * (x + h))) =>
(x - x - h) / (x * (x + h)) =>
(-h) / (x * (x + h))

Divide that all by h

-h / (x * h * (x + h)) =>
-1 / (x * (x + h))

actually ur question is wrong,but i think lim h->0 or any other limiting value should be specified.anyway if the question was lim h->0[1/(x+h) - 1/x]/h then answer is lim h->0[ [x- (x+h)]/x(x+h)]/h
=
lim h->0 (-h/h)*1/x(x+h) = -1/x^2 (put h=0) = -x^(-2).

[1/(x+h)-1/x]/h=
=(x-(x+h)]/[(x+h)x])/h=
=-h/[h(x+h)x]=
=-1/[(x+h)x]

lim(h-->0) -1/[(x+h)x]=-1/x^2

=>[1/(x+h)-1/x]/h
=>h/(x+h) -h/x
=>h/x+h/h-h/x
=>h/h+h/x-h/x
=>h/h
=>1