Answer
$\dfrac{3}{x-2} $
Work Step by Step
We apply Method 1 (A51), to treat the numerator and denominator of the complex rational expression separately. So by factoring both the denominator and numerator of each rational function and cancelling the common factors, we have
$$
\frac{\frac{x-2}{4x}}{\frac{x^2-4x+4}{12x}}= \frac{\frac{x-2}{4x}}{\frac{(x-2)^2}{12x}}= \frac{x-2}{4x}\frac{12x}{(x-2)^2}\\
=\frac{3}{x-2}
.$$
