Question

find difference quotient

f(x) = 1/x+3

Answer 1

recall that the difference quotient is (f(x+h)-f(x))/h
so just plug in your values

(1/(x+h+3) - 1/(x+3))/h
=
((x+3) - (x+h+3))/(x+h+3)(x+3)
---------------------------------------------
h

= (-h)/((x+h+3)(x+3)(h))
= -1/((x+h+3)(x+3)