Answer
$-\frac{1}{x(x+6)}$.
Work Step by Step
The given expression is
$=\frac{\frac{1}{x+6}-\frac{1}{x}}{6}$
Multiply the numerator and the denominator by $x(x+6)$.
$=\frac{x(x+6)}{x(x+6)}\cdot \frac{\frac{1}{x+6}-\frac{1}{x}}{6}$
Use the distributive property.
$=\frac{x(x+6)\cdot \frac{1}{(x+6)}-x(x+6)\cdot\frac{1}{x}}{6x(x+6)}$
Simplify.
$=\frac{x-(x+6)}{6x(x+6)}$
$=\frac{x-x-6}{6x(x+6)}$
$=\frac{-6}{6x(x+6)}$
$=-\frac{1}{x(x+6)}$.
