Write each rational expression in simplest form. State all restrictions on the variables
−12x^3 / 3x^2−3x
To simplify the rational expression −12x^3 / 3x^2−3x, we can cancel out common factors in the numerator and denominator.
The numerator −12x^3 can be factored as −12x^2 * x, while the denominator 3x^2−3x can be factored as 3x(x−1).
Cancelling out the common factors of x in the numerator and denominator, we get:
−12x^2 / 3(x−1)
To simplify this further, we can divide both the numerator and denominator by 3:
−4x^2 / (x−1)
Therefore, the simplified form of the rational expression is −4x^2 / (x−1).
Restrictions on the variable x:
The denominator (x−1) cannot equal zero, as division by zero is undefined. Therefore, x cannot equal 1. In other words, the restriction on the variable x is x ≠ 1.