Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 103: 25

$$ f(-2+h)=\frac{1}{-2+h}$$ $$\frac{f(a+h)-f(a)}{h}= -\frac{1}{3}$$

Since $ f(x)=\frac{1}{x}$, then $ f(-2+h)=\frac{1}{-2+h}$. The quotient difference is given by $$\frac{f(a+h)-f(a)}{h}=\frac{f(-1.5)-f(-2)}{0.5}=\frac{-\frac{1}{1.5}+\frac{1}{2}}{0.5}=-\frac{1}{3}$$