Answer
$$
f(x) =\frac{1}{x}
$$
(a)
$$
f(x+h) =\frac{1}{x+h}
$$
(b)
$$
\begin{aligned} f(x+h)-f(x) =\frac{-h}{x(x+h)} \end{aligned}
$$
(c)
$$
\begin{aligned} \frac{f(x+h)}{h} =\frac{-1}{x(x+h)} \end{aligned}
$$
Work Step by Step
$$
f(x) =\frac{1}{x}
$$
(a)
$$
f(x+h) =\frac{1}{x+h}
$$
(b)
$$
\begin{aligned} f(x+h)-f(x) &=\frac{1}{x+h}-\frac{1}{x}
\\ &=\left(\frac{x}{x}\right) \frac{1}{x+h}-\frac{1}{x}\left(\frac{x+h}{x+h}\right) \\ &=\frac{x-(x+h)}{x(x+h)} \\ &=\frac{-h}{x(x+h)} \end{aligned}
$$
(c)
$$
\begin{aligned} \frac{f(x+h)}{h} &=\frac{1}{h}\left[\frac{-h}{x(x+h)}\right] \\ &=\frac{-1}{x(x+h)} \end{aligned}
$$
