Precalculus (6th Edition) Blitzer

The expression $\frac{f\left( x+h \right)-f\left( x \right)}{h},\text{ }h\ne 0$ , is called the difference quotient of the function f. We find the expression by replacing x with $x+h$ each time x appears in the function’s equation. Then we subtract $f\left( x \right)$. After simplifying, we factor h from the numerator and divide out identical factors of h in the numerator and denominator.