Answer
$\displaystyle \frac{7}{10}$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$ \displaystyle \frac{4}{x-6}\div\frac{40}{7x-42}=\frac{4}{x-6}\cdot\frac{7x-42}{40}\qquad$... factor what you can
$=\displaystyle \frac{4}{x-6}\cdot\frac{7(x-6)}{40}\qquad$... divide out the common factors
$=\displaystyle \frac{1}{1}\cdot\frac{7(1)}{(10)}\qquad$
= $\displaystyle \frac{7}{10}$
