Answer
$\displaystyle \frac{1}{4}$
Work Step by Step
$\displaystyle \frac{2k-16}{6}\div\frac{4k-32}{3}=\qquad$
... apply property:$ \displaystyle \frac{P}{Q}\div\frac{R}{S}=\frac{P}{Q}\cdot\frac{S}{R} $
$=\displaystyle \frac{2k-16}{6}\cdot\frac{3}{4k-32}$
... factor out 2 in the first numerator,
... factor out 4 in the second denominator
$=\displaystyle \frac{2(k-8)}{6}\cdot\frac{3}{4(k-8)}= \qquad$
... apply property: $\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS}$
$=\displaystyle \frac{2\cdot 3(k-8)}{2\cdot 3\cdot 4(k-8)}\qquad$... reduce: 2, 3, $(k-8)$
$=\displaystyle \frac{1}{4}$
