Answer
$\dfrac{x^{2}-4}{24x}\div\dfrac{2-x}{6xy}=-\dfrac{y(x+2)}{4}$
Work Step by Step
$\dfrac{x^{2}-4}{24x}\div\dfrac{2-x}{6xy}$
Factor the numerator of the first fraction:
$\dfrac{x^{2}-4}{24x}\div\dfrac{2-x}{6xy}=\dfrac{(x+2)(x-2)}{24x}\div\dfrac{2-x}{6xy}=...$
Evaluate the division of the two rational expressions and simplify by removing factors that appear both in the numerator and the denominator. To remove $(x-2)$ and $(2-x)$, change the sign of $(2-x)$, and the sign of the fraction:
$...=\dfrac{6xy(x+2)(x-2)}{24x(2-x)}=-\dfrac{6xy(x+2)(x-2)}{24x(x-2)}=...$
$...=-\dfrac{6y(x+2)}{24}=-\dfrac{y(x+2)}{4}$
