Final answer:
To simplify the expression (4x^4 - 6x^3 - 12x + 12)/(4x - 6), factor out the numerator and denominator, then cancel out the common factors.
Step-by-step explanation:
To simplify the expression (4x^4 - 6x^3 - 12x + 12)/(4x - 6), we need to factor out the numerator and the denominator. First, let's factor out the numerator:
(4x^4 - 6x^3 - 12x + 12) = 2(2x^3 - 3x^2 - 6x + 6)
Now let's factor out the denominator:
(4x - 6) = 2(2x - 3)
Next, we can cancel out the common factors:
(2(2x^3 - 3x^2 - 6x + 6))/(2(2x - 3))
Finally, we have:
(2x^3 - 3x^2 - 6x + 6)/(2x - 3)