Difference quotient for $$$f{\left(x \right)} = \frac{2}{x}$$$

Find the difference quotient for $$$f{\left(x \right)} = \frac{2}{x}$$$.

The difference quotient is given by $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h}$$$.

To find $$$f{\left(x + h \right)}$$$, plug $$$x + h$$$ instead of $$$x$$$: $$$f{\left(x + h \right)} = \frac{2}{x + h}$$$.

Finally, $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\frac{2}{x + h} - \frac{2}{x}}{h} = - \frac{2}{x \left(h + x\right)}$$$.

The difference quotient for $$$f{\left(x \right)} = \frac{2}{x}$$$A is $$$- \frac{2}{x \left(h + x\right)}$$$A.