Answer
$a)$ $f(x+h)=\frac{1}{x+h}$
$b)$ $f(x+h)-f(x)=\frac{-h}{(x+h)x}$
$c)$ $\frac{f(x+h)-f(x)}{h}=-\frac{1}{(x+h)x}$
Work Step by Step
$a)$
$$f(x)=\frac1x$$
Replace $x$ with $x+h$:
$$f(x+h)=\frac{1}{x+h}$$
$b)$
$$f(x+h)-f(x)$$
Substitute corresponding expressions:
$$\frac{1}{x+h}-\frac1x$$
$$\frac{x-(x+h)}{(x+h)x}=\frac{x-x-h}{(x+h)x}=\frac{-h}{(x+h)x}$$
$c)$
$$\frac{f(x+h)-f(x)}{h}$$
Substitute corresponding expression for numerator:
$$\frac{\dfrac{-h}{(x+h)x}}{h}=-\frac{1}{(x+h)x}$$
