Answer
$\left(\frac{g}{h}\right)(x) = \dfrac{(x - 2)(x + 2)}{2(2x - 3)}$
Work Step by Step
Divide $g(x)$ by $h(x)$:
$\left(\frac{g}{h}\right)(x) = \dfrac{x^2 - 4}{4x - 6}$
Factor the numerator by using the difference of two squares formula:
$x^2 - 4 = (x - 2)(x + 2)$
Factor the denominator by factoring out $2$ as the greatest common factor of the two terms:
$4x - 6 = 2(2x - 3)$
Put the two expressions back into fraction form:
$\left(\frac{g}{h}\right)(x) = \dfrac{(x - 2)(x + 2)}{2(2x - 3)}$
