Answer
$\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2x-12}{8x^{2}}=x(x+4)$
Work Step by Step
$\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2x-12}{8x^{2}}$
Take out common factor $2$ in the numerator of the second fraction:
$\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2x-12}{8x^{2}}=\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2(x-6)}{8x^{2}}=...$
Evaluate the division of the two rational expressions:
$...=\dfrac{8x^{2}(x-6)(x+4)}{8x(x-6)}=...$
Simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{8x^{2}(x+4)}{8x}=x(x+4)$
