What is the quotient 4−xx2−2x−3÷x2−4xx2−x−6 in simplified form? State any restrictions on the variable
To simplify the quotient, we first perform long division:
4 − x x² - 2x - 3
______________________
x² - 4x x² - x - 6
- (x² - 4x)
___________
4x - 3
- (4x - 2)
___________
- 1
Therefore, the quotient is x - 1.
Restrictions on the variable x:
The divisor cannot be equal to zero, so x² - x - 6 ≠ 0. This quadratic equation can be factored into (x - 3)(x + 2) = 0, which means x cannot be equal to 3 or -2.
So, the restrictions on the variable x are x ≠ 3 and x ≠ -2.