Chapter 1 - Functions and Their Graphs - Section 1.1 Functions - 1.1 Assess Your Understanding - Page 55: 80

$\frac{-1}{(x+3)(x+h+3)}$

Step 1. $f(x+h)=\frac{1}{x+h+3}$ Step 2. $f(x+h)-f(x)=\frac{1}{x+h+3}-\frac{1}{x+3}=\frac{x+3-(x+h+3)}{(x+3)(x+h+3)}=\frac{-h}{(x+3)(x+h+3)}$ Step 3. $\frac{f(x+h)-f(x)}{h}=\frac{-1}{(x+3)(x+h+3)}$